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AN   ESSAY 


THE   MEANS  AND  IMPORTANCE 


UVTRODIJCIIVG  THE  IVATURAL  SCIEWCES 


THE    PAMILTf-LIBRARY, 


DIFFUSING  THE  ELEMENTS  OF  GEOMETRY 


THE  PLAN  OF  THE  POPULAR  EDUCATION: 
By  D.jjMcCURDY, 

LATE   A   CLERK   IN   THE   U.  S.  PENSION   OFFICE. 


SECOND   EDITION,   IB(rt>ROVED. 


WASHINGTON: 

BLAIR  AND  RIVES,  PRINTERS. 

1842. 


4-J^^-    \ 


CAJORI 


Entered,  according  to  act  of  Congress,  in  the  Clerk's  office  of  the  District  of 
Columbia,  by  Dennis  McCurdy. 


Note. — An  error  in  the  orthography  of  this  author's  name  was  uninten- 
tionally admitted  into  the  former  edition  of  this  Essay.  The  remarks  made 
in  connection  with  that  error  were  intended  for  another  occasion. 


'''  Lhli.^ 


A 


;  o  / 


RECOMMENDATIONS. 


The  writer  of  the  following  discursive  remarks  served  the  republic  during 
twenty-two  years,  die  et  nocte,  as  a  teacher,  in  word  and  sign ;  commissioned 
and  caressed  by  the  people  long  before  the  strength  of  the  young  men  had 
gone  forth  from  the  halls  of  the  muses  to  disseminate  literature  and  science 
in  the  land.  Then,  in  1834,  after  a  suspension  of  two  years  or  more,  06- 
•casioned  by  disease,  the  effect  of  his  application,  he  was  employed  as  a  clerk 
in  the  service  of  the  government ;  and,  in  1840,  notified,  with  others,  that 
from  the  28th  of  February,  1841,  his  service  should  not  be  required.  The 
last  ten  years  have  presented  to  his  view,  unsought,  shades  of  human  charac- 
ter deeper  than  those  which  he  had  been  accustomed  to  contemplate ;  there- 
fore, with  incredible  pleasure,  he  returns  to  the  pursuits  of  Science,  because 
he  feels  within  himself  the  more  cordial  palpability  of  the  benign  radiance 
beaming  from  the  beauty  of  her  truths. 

Prom  many  flattering  testimonials  furnished  to  him  by  citizens  of  this  Dis- 
trict, in  orde/  to  favor  his  application  for  a  school  in  the  city  of  Baltimore,  he 
thinks  it  proper  to  select  for  publication  here  the  letter  received  from  the 
offic  ^  where  he  had  the  honor  to  serve  ;  for  the  public  service  is  honorable  in 
ilself;  but  the  manner  of  obtaining  «  place  may  be  antithetical,  and  the  fervid 
ambition,  incapacity,  &nd  catastrophe  of  Phaeton  are  recorded  for  our  instruc- 
tion. 

"  WASHINGTON,  July  30,  1841. 
"  We  hereby  certify  that  Mr.  Dennis  McCorby  has  been  a  clerk  in  the 
Pension  Office  for  several  years,  and  is  now  dropped  in  consequence  of  the 
decrease  of  the  business.  During  his  continuance  in  office,  we  have  neces- 
sarily acquired  a  knowledge  of  his  attainments ;  and  do  most  earnestly  and 
unhesitatingly  recommend  him  to  the  Commissioners  of  the  Public  Schools 
in  Baltimore,  as  possessing  high  and  eminent  qualifications  as  an  instructor. 

"  GEO.  W.  CRUMP,  Chief  Clerk. 

"  JOHN  D.  WILSON,  Clerk. 

•«  HENRY  H.  SYLVESTER,  Clerk. 

'•  WM.  S.  ALLISON,  Clerk. 

♦•  FRENCH  S.  EVANS,  CUrk. 

"  DANIEL  BROWN,  Clerk. 

"  JAMES  L.  EDWARDS, 

*'  Commissioner  of  Pensions." 

The  appointment  in  Baltimore  was  made  in  favor  of  a  worthy  gentleman, 
who  had  the  greatest  minority  of  votes  at  a  preceding  election  for  teacher. 
And,  on  application  to  be  reinstated  as  a  clerk,  the  President  of  the  United 
States  made  the  following  endorsement  of  the  papers  submitted  to  him  on  our 
behalf; 


„M 


6 

dured  their  scorn,  until  by  pertinacity  he  drew  the  current 
of  public  opinion  into  his  ship's  path  over  the  previously  un- 
explored deep.  Upon  men  without  fortune  has  always  de- 
volved the  labor  of  instructing  the  world. 

Such  is  the  example  which  we  propose  to  ourselves  in 
urging  the  improvement  of  common  school  education,  by  the 
infusion  of  the  elements  of  geometry.  For  this  purpose,  a 
plan  of  a  Manual  and  Chart  is  proposed :  a  description  of 
which  may  be  seen  in  a  subsequent  part  of  this  Essay.  But, 
in  order  to  place  the  means  of  acquiring  the  knowledge  of 
science  in  the  way  of  adults  of  both  sexes,  we  here  present  a 
prospectus  of  a  Magazine,  which  may  be  imitated  by  men  of 
science  in  all  practicable  places.  A  periodical  publication, 
commencing  with  the  elements  of  geometry  and  arithmetic, 
and  containing  a  well-arranged  and  complete  course  of 
mathematics,  would  be  read,  in  many  instances,  by  persons 
who  could  never  be  persuaded  to  undertake  the  subject  by 
means  of  the  books  used  in  schools  ;  especially  if  the  illus- 
trations should  be  so  simplified  as  to  supply  the  want  of  living 
teachers.  Such  reading,  exclusive  of  the  practical  use  of  the 
sciences,  would  contribute  to  neutralize  the  deleterious  ef- 
fects of  works  of  fiction,  ultra  politics,  and  all  that  exuber- 
ance of  fanciful  matter  by  which  the  morals  of  the  age  are 
relaxed,  and  the  line  traversed  in  every  direction,  which  dis- 
tinguishes  right  from  wrong.  The  reports  of  the  many 
violations  of  law  and  order  would  not  be  read  for  amusement, 
which  is  a  certain  patronage  of  the  wrong-doer ;  the  brightest 
parts  would  not  be  employed  in  depicting  the  vices  and  fol- 
lies of  men  with  a  playful  coloring  of  their  enormity,  from 
which  the  fascinated  reader  glides,  among  the  puppets  of  the 
author,  into  those  errors  which  he  finds  so  elegantly  described. 
The  rule  of  right,  upon  which  the  eye  of  the  freeman  should 
ever  be  fixed,  is  not  laid  down  in  such  productions.  The 
false  impression  is  not  effaced  from  the  reader's  mind,  that 
he  is  not  accountable  to  God  or  his  country  until  after  he 
has  entered  his  or  her  service  by  special  agreement,  and 
signed  a  pledge,  or  made  profession  to  that  effect.  If  the 
author  is  friendly  to  religion,  he  must  disguise  that.  To 
acknowledge  the  claim  of  the  Redeemer  to  the  love  of  our 
race,  is  an  insuperable  barrier  to  that  friendship.  His  regard 
for  good  morals  also  wants  the  rule — "  To  love  one's  neighbor 
as  himself."  Hence  such  writings  do  not,  in  any  instance, 
reprove  the  reader  for  faults,  nor  afford  any  light  for  the  cor- 
rection of  errors  ;  which,  after  all,  are  mere  negative  utilities. 
And  thus  failing  in  the  first  part  of  the  rule  of  improvement — 


<•  Cease  to  do  evil,"  they  can  have  no  pretensions  whatever  to 
the  second  part — "Learn  to  do  well."  Having,  therefore, 
neither  positive  nor  negative  goodness,  the  ahernative  is  evil; 
and,  under  these  views,  we  cannot  be  of  the  number  of  those 
who  would  regret  the  loss  of  reputation,  as  such,  to  writers  of 
this  class,  by  a  voyage  from  Europe  ;  because,  in  our  humble 
opinion,  that  loss  would  rather  be  the  recovery  of  sound  dis- 
cretion to  a  portion  of  the  people,  who  had  been,  to  some  ex- 
lent,  deluded  by  the  misapplication  of  great  talents — a  reduc- 
tion of  over-rated  worth  to  its  par  value. 

There  is  also  another  object  to  be  achieved  by  the  diffusion 
of  the  exact  sciences,  (if  our  people  will  be  gratified  while 
the  Genius  of  our  institutions  weeps,  and  Modesty  shrinks 
from  the  scene,)  namely  :  to  make  the  amateurs  of  indecent 
exhibitions  intimate  with  the  properties  of  the  spiral  curve  ; 
that  they  may,  at  least,  be  able  to  criticise,  with  fastidious  ac- 
curacy, the  circumgyrations  of  all  young  dancers,  patented  at 
the  courts  of  dukes  and  princes,  as  one  of  the  means  of  gov- 
erning their  disfranchised  canaille^  whose  return  to  sound 
discretion  these  magnates  might  have  some  cause  to  dread  ; 
but  who  are  entirely  useless  to  our  people  in  the  administra- 
tion of  their  affairs,  either  private  or  public.  Useless,  indeed, 
and  inefficient  for  any  purpose  of  good,  but  greatly  prohfic 
as  the  seed  of  evil ;  because  the  arfist,  corrupt  at  heart,  and 
ready  to  sell  his  country  for  sordid  gain,  exhibits  for  sale 
multiplied  copies  of  such  indelicate  exposures ;  and,  in  the 
interior  of  his  impure  shop,  finishes  the  work  of  shame  un- 
disguised, to  which  he  will  invite  the  ripening  debauchee, 
disgracing  humanity,  and  breaking  down  the  last  impediment 
which  obstructs  the  decline  of  virtue.  Where,  do  you  in- 
quire, are  the  seats  of  such  abominations?  Tamper  with 
the  crime  in  your  theatres,  and  you  will  find  the  copies  every 
where  in  the  streets  of  your  cities.  Their  favorite  [jaunts 
will  be  near  the  legislative  halls,  dishonoring  the  precincts  of 
the  sacred  fanes  of  human  liberty,  without  the  remedy  of 
law,  or  a  vindicator  of  the  public  sanctity.  For  how  will 
your  courts  be  able  to  convict  or  punish  in  the  copy  that 
which  you  have  sanctioned  and  applauded  in  the  original? 
Citizens  !  will  you  make  the  fine  arts  the  medium  of  cor- 
rupting your  morals  ?  Will  you  abdicate  your  rational  forms 
of  government,  and  be  led  by  low  sensations  unbecoming  the 
supreme  dignity  of  the  inheritance  of  your  philosophic  and 
Christian  fathers?  Will  you  borrow  your  taste,  as  a  people, 
from  the  kennels  of  paganism,  perpetuated  as  it  is  in  the 
unamended  condition  of  a  large  majority  of  the  populace  of 
the  old  world  ? 


s 

THE  WASHINGTON  MAGAZINE, 

AND 

JUNIOR     citizens'    GUIDE    TO    SCIENCE, 

BY  D.  MgCURDY  &  CO., 

Will  be  issued  monthly,  at  $b  per  annum,  payable  in  advance,  making 
an  annual  volume  of  nearly  600  octavo  pages,  with  a  plate  of  the  appropriate 
diagrams  to  accompany  each  number. 

It  will  contain  a  regular  course  of  Mathematics,  commencing  with  the 
Elements  of  Geometry  and  Arithmetic,  in  separate  departments,  and  followed 
by  Plane  Trigonometry  and  Algebra,  the  art  of  constructing  Logarithms, 
Surveying  and  practical  Navigation,  Geometry  of  Solids  and  Mensuration, 
Spherical  Trigonometry,  Conic  Sections,  and  Astronomv,  Carpentry,  the 
Mechanics'  Price  Book,  and  Plans  of  Modern  Buildings,  Architecture, 
Civil  Engineering,  Mechanical  Philosophy,  &c.,  &c.  It  may  be  remarked 
that  several  of  these  and  other  branches  differ  only  in  name  and  applica- 
tion; that  the  general  principles  are  common  to  many  of  them,  and  that 
the  labor  of  acquiring  the  knowledge  of  the  course  is  less  than  may  be 
generally  supposed  :  the  principal  hinderance  consists  in  the  impatient  haste 
to  pass  over  the  first  principles  with  the  absurd  question,  "What  use  is 
there  in  that  r' 

The  most  approved  authorities  will  be  consulted,  and  the  named  Editor's 
long  experience  in  teaching  will  be  put  in  requisition  for  the  benefit  of  those 
citizens  who  have  to  contend  with  the  crude  materials  of  Nature  in  organiz- 
ing the  habitable  world.  It  is  not  intended  to  pass  with  a  light  saltation  from 
one  branch  of  the  tree  of  natural  knowledge  to  another,  but  to  investigate  the 
permeant  elements  in  their  course  through  the  trunk,  branches,  flowers,  and 
fruit ;  and  to  exhibit  in  the  foreground  whatever  tends  more  immediately  to  the 
increase  of  human  skill  and  power.  Each  particular  branch  will  be  based 
upon  a  sufiicient  number  of  theorems  duly  demonstrated,  and  illustrated  by 
the  necessary  problems  to  meet  the  several  cases  which  those  theorems  may- 
embrace  ;  but  where  different  branches  rest  upon  the  same  theorems,  these 
latter  will  not  be  repeated. 

In  order  to  consociate  amusement  with  instruction,  the  leading  principles 
and  rules  of  grammar,  rhetoric,  and  logic  will  be  inserted ;  and  a  chapter 
on  the  art  and  forms  of  keeping  accounts;  also  a  succinct  historical  account 
of  the  progressive  improvements  in  the  sciences,  and  a  brief  biograp^hy  of 
eminent  mathematicians,  will  be  introduced  at  proper  intervals  in  the  work ; 
and,  that  all  classes  of  readers  may  be  gratified,  popular  descriptions  will  be 
given  of  the  natural  and  other  curiosities  contained  in  the  National  Gallery ; 
also  a  regular  account  of  the  most  important  transactions  of  the  National 
Institution,  recently  established  in  the  city  of  Washington. 

The  Washington  Magazine  will  be  a  family  instructor  of  the  cheapest 
kind ;  and  a  useful  companion  for  the  retirement  of  young  men  preparing 
themselves  for  high  distinction  in  the  national  mart.  Therefore,  to  extend 
the  advantages  of  science,  the  remittance  of  S20  from  any  college,  academy, 
village,  military  or  fire  company,  community  or  association,  in  the  same  let- 
ter, will  be  received  in  full  for  live  copies  of  the  Magazine;  and  in  the  same 
ratio  for  a  greater  number.  The  postmaster  certifying  the  enclosure  will 
make  us  responsible.    The  postage  must  be  paid,  or  the  letter  franked. 

Remittances  may  be  made,  in  good  money,  to  D.  Clagett,  Esq.,  merchant, 
Washington,  D.  C. ;  Benjamin  Hailowell,  Esq.,  Alexandria,  D.  C;  or  Alex- 
ander Yearley,  Esq.,  Baltimore,  Maryland. 


AN  ESSAY. 


The  desire  to  diffuse,  or  rather  to  accumulate,  knowledge, 
has  recently  received  a  simultaneous  impulse  from  many 
points  ;  and  the  best  talents  in  the  world  are  concentrating 
their  thoughts  on  the  metropolis  of  this  Union,  to  render  it 
the  Emporium  of  Science.  Here  the  lines  converge ;  the 
march  is  onward,  and  no  power  at  this  time  can  retard  its 
speed.  The  wisdom  of  men  will  consist  in  regulating  and 
directing  the  momentum  to  the  safest  and  happiest  results, 
in  promoting  the  contentment  and  industry  of  the  people, 
and  in  preserving  the  due  equilibrium  of  power  by  equal 
education,  so  as  to  ensure  the  faithful  execution  of  the  laws. 
We  shall  just  notice  a  few  of  the  most  prominent  indications 
of  the  desire  referred  to  above,  in  order  to  show,  in  the  out- 
set, the  increasing  importance  of  diffusing  the  elements  of 
science  more  equally  among  the  people. 

Indications  of  the  desire  to  diffuse  knowledge  : 

1.  In  the  action  of  Congress  with  regard  to  the  bequest  of 
Mr.  Srnithson. 

2.  In  the  establishment  of  the  National  Institution  at 
Washington. 

3.  In  the  action  of  the  friends  of  popular  education  in 
some  of  the  States,  resulting  from,  the  disclosures  made  in 
the  last  ceyisus. 

1.  The  Congress  of  the  United  States  have  assumed  a 
trust,  in  the  case  of  the  Smithsonian  bequest,  under  which 
they  are  pledged  to  establish,  in  the  city  of  Washington,  an 
institution  for  the  diffusion  of  knowledge  among  men.  To 
this  undertaking,  divested  of  any  evil  tendency,  we  wish 


10 

ail  possible  celerity  and  success.  It  may  be  rendered  use- 
ful; but,  like  the  Grecian  gift,  it  may  introduce  treason 
into  the  citadel  of  our  liberties,  by  teaching  us  to  love  gifts, 
to  depend  upon  contingencies,  and  be  the  less  blessed  of 
the  two  cases — namely,  that  of  the  receiver  and  that  of 
the  giver.  Our  own  resources  properly  employed  are  suf- 
ficient for  our  wants.  Giving  to  this  testator's  views  the 
best  construction,  the  bequest  is  a  high  compliment  to 
our  institutions,  and  to  us  a  memento  to  persevere  in  that 
moderation  which  is  the  true  characteristic  of  a  people  who 
are  willing  to  do  right — who  require  only  the  light^  not  the 
compulsive  power  of  the  law.  In  this  view  of  the  case,  the 
trust,  it  must  be  admitted,  is  worthy  of  a  free  people,  and 
their  representatives  are  in  every  respect  adequate  to  its  ex- 
ecution. From  the  assumption  of  this  trust,  however,  as 
well  as  from  the  annual  appropriations  for  the  support  of 
their  military  academy,  and  the  many  excellent  documents 
which  are  sent  out  from  the  halls  of  legislation  at  public 
expense,  it  is  plain  that  Congress  do  not  mean  to  admit  any 
constitutional  or  other  restriction  of  their  power  to  diffuse 
knowledge.  This  is  a  gratifying  disposition  in  the  Legis- 
lature, to  which  we  may  hereafter  advert  in  the  course  of 
these  remarks. 

But  with  respect  to  the  species  of  knowledge  to  be  dif- 
fused under  the  trust,  there  are  various  opinions.  It  is  con- 
tended, in  this  case,  that  no  kind  of  knowledge  is  proper 
which  our  citizens  owe  to  themselves  or  their  children  ;  for 
this  we  should  furnish  at  our  own  expense.  This  view,  it 
will  be  perceived,  excludes  every  branch  of  useful  know- 
ledge ;  because  all  such  we  owe  to  ourselves  and  our  chil- 
dren, and  more  as  a  reigning  people  than  we  should  as  a 
subject  people.  Besides,  we  owe  to  the  world  as  much  as 
any  other  member  of  the  family  of  nations,  under  the  great 
Father  of  the  universe.  Is  not  our  portion  of  the  common 
inheritance  equal  to  that  of  any  other,  nay,  better  than  others? 
Has  he  not  assigned  to  us  from  his  table  a  Benjamin's  mess? 


11 

Shall  we  then  insult  the  Fountain  of  Light  by  admitting  only 
a  few  rays,  jnst  sufficient  to  cause  obliquity  of  vision,  and 
qualify  us  to  take  delight  in  short-lived  and  local  scenes? 
The  people  owe  it  to  themselves  to  repel  all  suggestions  to 
restrict  or  circumscribe  their  pursuit  of  knowledge ;  and 
every  man  should  extend  his  sphere  as  far  as  may  comport 
with  the  means  and  time  he  can  honestly  devote  to  its  ac- 
quisition. Knowledge  is  the  true  lever  of  equality  which 
can  elevate  the  ponderous  mass,  and  as  such  we  are  anx- 
ious to  recommend  it  to  all.  We  also  believe  that  Congress 
may  constitutionally  erect  an  observatory  at  the  nation's 
expense,  and  found  a  national  institution  embracing  the 
ample  range  of  the  sciences  and  arts ;  that  they  ought  to  do 
so  forthwith ;  and  that  the  honor  and  dignity  of  the  republic 
are  compromised  in  the  delay. 

2.  Another  indication  of  the  desire  to  diffuse  knowledge 
is  clearly  developed  in,  the  establishment  of  an  association 
at  the  city  of  Washington,  in  May,  1840,  under  the  denom- 
ination of  the  National  Institution.  The  object  of  this  in- 
stitution is  to  promote  science  and  the  useful  arts.  The 
number  of  its  members  already  exceeds  six  hundred,  and 
the  increase  is  constant.  The  initiation  fee  is  five  dollars, 
and  the  annual  contribution  is  the  same  amount.  Its  mem- 
bers are  resident,  corresponding,  and  a  few  honorary.  The 
President  of  the  United  States  is  called  the  patron  of  the 
institution ;  it  has  a  president,  the  Hon.  Joel  R.  Poinsett ; 
vice  president,  Peter  Force,  Esq. ;  twelve  directors,  of  which 
six  are  elected  by  the  institution,  and  the  other  six  are  the 
members  of  the  cabinet  at  Washington  ;  namely,  the  four 
Secretaries,  the  Postmaster  General,  and  the  Attorney  General. 
The  directors  on  the  part  of  the  institution,  at  present,  are 
the  Hon.  Levi  Woodbury  and  Hon.  William  0.  Preston, 
Senators;  Col.  J.  J.  Abert,  chief  of  the  topographical  en- 
gineer bureau ;  Col.  Joseph  Totten,  chief  of  the  engineer 
bureau ;  A.  O.  Dayton,  Fourth  Auditor  of  the  Treasury ; 
and  Com.  L.  Warrington,  one  of  the  Commissioners  of  the 


12 

Navy  Board.  Francis  Markoe,  jr.,  Esq.,  is  the  correspond- 
ing secretary;  G.  R.  Barry,  Esq.,  recording  secretary;  and 
Dr.  H.  King  is  the  curator  of  the  institution.  The  subjects 
of  research  are  divided  into  eight  classes,  namely,  astron- 
omy, geography,  and  natural  philosophy  ;  natural  history  ; 
geology  and  mineralogy ;  chemistry ;  the  application  of  sci- 
ence to  the  useful  arts  ;  agriculture ;  American  history  and 
antiquities ;  literature  and  the  fine  arts.  Besides  the  nume- 
rous specimens  of  geology,  mineralogy,  and  other  objects 
of  natural  history  collected  by  the  members,  the  association 
has  in  charge  the  immense  variety  of  curiosities  sent  home 
by  the  exploring  expedition.  The  correspondence  of  this 
institution  already  extends  to  all  parts  of  the  world,  and  its 
present  condition  is  highly  pleasing  and  prosperous.  Its  * 
depository  is  the  new  national  gallery — one  of  the  rarest 
specimens  of  architecture,  and  said  to  be  the  most  spacious 
room  in  the  United  States.  We  propose  to  give,  in  the 
fixture  numbers  of  our  contemplated  magazine,  a  fuller  ac- 
count of  the  transactions  of  this  institution,  and  a  classified 
description  of  the  astonishing  collection  of  the  productions 
of  nature  and  art,  civilized  and  savage,  placed  in  charge  of 
the  curator  of  the  institution.  Dr.  King. 

3.  The  last  indication  of  the  growing  desire  to  diffuse 
knowledge  which  we  shall  here  notice,  is  the  action  of  the 
friends  of  science  in  the  States,  impelled  by  the  disclosure 
resulting  from  the  statistics  collected  in  the  taking  of  the 
last  census.  It  appears  that  many  of  the  people  are  desti- 
tute of  all  literary  knowledge,  and  large  masses  of  the  com- 
munity receive  but  a  very  limited  education.  This  action 
will  be  the  more  effectual,  because  it  carries  the  remedy  to 
the  seat  of  the  disease.  When  the  people  undertake  to  do 
their  own  work,  it  will  be  done.  The  lark,  in  the  fable, 
thought  it  unnecessary  to  remove  her  young  from  the  wheat - 
field  while  the  farmer  depended  on  neighbors  or  friends  for 
his  reaping ;  but  when  he  concluded  to  begin  by  himself 
on  the  morrow,  she  exhorted  her  little  brood  to  provide  for 


13 

their  future  safety.  There  will  be  no  more  delay  in  this  dif- 
fusion of  knowledge,  since  the  proper  agents  are  to  be  em- 
ployed. We  are,  however,  constrained  to  express  the  hope, 
that  the  basis  of  whatever  system  they  may  adopt  will  em- 
brace the"  elements  of  geometry,  as  being  necessary  for  the 
support  of  any  superstructure  which  can  avail  in  erecting 
the  minds  of  the  people. 

Astronomy^  which  leads  the  whole  train  of  the  sciences^  is 
dependent  on  the  elements  of  geometry. — The  National  In- 
stitution, as  appears  from  the  preceding  aiTangement,  has 
very  properly  placed  astronomy  at  the  head  of  its  list  of  the 
natural  sciences.     This  is  the  study  which  first  inspired 
man  with  the  spirit  of  inquiry,  and  for  the  sake  of  which 
the  subordinate  sciences  have  been  intensely  prosecuted. 
Dedit  homini  sid)lime  os.     In  its  modern  improvements, 
the  application  of  its  principles   descends  even  to  regu- 
late the  weights  and  measures  in  the  hands  of  the  mer- 
chant.    It  sweeps  the  cerulean  expanse  with  the  telescope, 
watches  the  motions  of  the  heavenly  bodies,  and  collects 
its   data  from  a  thousand  stations  at  a  thousand  dates; 
adding  to  the  number  of  celestial  discoveries  such  revolu- 
tions and  phases  as  the  planets  and  satellites  exhibit  from 
any  peculiarity  of  the  observer's  position  with  regard  to  the 
ecliptic,  or  highway  of  the  distant  worlds.     "  And  never," 
says  the  Hon.  Joel  R.  Poinsett,  late  iSecretary  of  War,  and 
senior  director  of  the  National  Institution,  in  his  excellent 
discourse  delivered  at  its  first  anniversary,  "  never  has  been 
commenced  a  monument  to  the  glory  of  science  and  humsui 
intellect  more  sublime  than  that  of  which  astronomy  is  now 
laying  the  foTindation."    "Shall  we  not  add,"  continues 
Mr.  P.,  "  one  stone  to  the  structure?    Will  we  expose  our- 
selves to  be  denied  our  just  title  of  a  moral,  intelligent,  and 
enlightened  people,  by  refusing  to  inscribe  the  United  States 
of  America  among  the  names  of  the  civilized  nations  of  the 
earth,  which  will  be  found  engraved  upon  the  columns  of 
this  magnificent  temple?    Are  we  not  a  navigating  and 


14 

commercial  people  ?  Does  not  our  flag  float  on  every  sea, 
and  visit  every  accessible  region  of  the  world  ?  And  shall 
we  not  have  our  national  observatory,  our  astronomical 
archives,  and  our  celestial  ephemeris  [day-book]?  Shall  we 
any  longer  leave  our  navigators  exposed  to  the  disgrace  of 
acknowledging  that,  without  the  astronomical  ephemerides 
published  in  Europe,  they  could  not  with  safety  navigate 
distant  seas?  I  hope  not."  And  so,  to  echo  the  pious  as- 
piration, we  all  hope.  Nevertheless,  whatever  praise  may 
be  due  to  the  noble  science  of  astronomy,  no  practical 
utility  can  accrue  to  the  community  from  it,  without  a  pre- 
vious knowledge  of  geometry,  upon  the  principles  of  which 
astronomy  must  be  superinduced.  It  is,  therefore,  our  in- 
tention, in  the  humble  office  of  pioneer,  to  co-operate  with 
the  magnanimous  designs  of  this  excellent  institution,  by 
disseminating  the  elements  of  science  more  generally  among 
the  people;  without  which  they  must  come  unprepared, 
though  invited,  to  the  intellectual  feast. 

The  same  elegant  writer  and  true  patriot,  in  speaking  of 
the  science  of  technology,  or  the  union  of  scientific  knowl- 
edge with  mechanical  skill,  instances  the  case  of  James 
Watt,  LL.D.,  who  invented  the  steam-engine,  the  most  per- 
fect of  human  devices,  "  a  present,"  so  called,  "  from  science 
to  the  arts."  And  the  case  of  Peter  Dolland,  who  accom- 
plished  through  this  Union,  what  even  Newton  had  given 
up  as  unattainable.  Mr.  P.  here  alludes  to  Dolland's  equa- 
torial instrument  for  correcting  the  errors  of  refraction  in  alti- 
tude, of  which  the  inventor  gave  to  the  Royal  Society  some 
account  in  1779.  The  discourse  here  alluded  to  furnishes 
an  outline  of  what  a  National  Institution  ought  to  be :  it  has 
been  distributed  gratuitously,  and  may  be  had,  we  believe, 
at  the  Patent  Office.  No  intelligent  citizen  should  omit  the 
perusal  of  this  valuable  pamphlet,  or  the  subscription  of  his 
name  to  the  National  Institution  therein  defined  and  recom- 
mended. 

A  Magazine  of  the  natural  sciences^  for  the  family  library , 


15 

should  co7nmence  loith  the  elements  of  arithmetic  and  geom- 
etry.— We  have  thus  briefly  adverted,  ad  res  gestas,  to  the 
things  done,  or  contemplated  to  be  done,  at  Washington, 
and  in  some  of  the  States,  for  the  diffusion  of  knowledge 
among  men.  We  desire  to  point  the  telescope  of  consider- 
ation to  the  hill  of  science  in  the  far,  elevated,  serene 
distance;  that  the  junior  multitude,  whom  we  would  rouse 
to  application,  may  have  some  idea  at  least  of  the  direc- 
tion in  which  we  propose  to  lead  them,  by  means  of  the 
magazine  which,  with  the  aid  of  the  friends  of  science, 
we  propose  to  publish.  But  as  in  the  outset  of  every  jour- 
ney some  preparation  is  demanded,  so  likewise  shall  we  be 
required  to  make  provision  for  the  way.  It  is,  however, 
peculiar  to  this  line  of  march,  that,  in  collecting  the  materi- 
als, our  progress  will  be  facilitated  ;  and  the  elements  which 
we  collect  will  be  no  impediment  to  the  celerity  of  our  ad- 
vancement: on  the  contrary,  the  more  we  collect,  the  more 
rapidly  shall  we  approach  the  object  at  which  we  aim.  Let 
these  remarks  be  now  applied  to  the  acquisition  of  the  ele- 
ments of  geometry  and  arithmetic,  without  the  aid  of  which 
no  progress  can  be  made  in  mathematical  knowledge ;  and 
let  it  be  understood  that  under  these  two  heads  are  all  the 
elements  of  the  exact  sciences  contained. 

Geometry  and  arithmetic  should  liave  priority  of  alge- 
bra.— Mathematical  reasoning  is  conducted  according  to  two 
methods, — one  is  called  the  method  of  analysis,  or  resolution; 
the  other,  the  method  of  synthesis,  or  composition.  Algebra 
adopts  the  former  of  these ;  separating  the  known  from  the 
unknown  parts  of  a  general  proposition;  representing  num- 
ber and  magnitude  by  symbols,  and  descending  by  a  suc- 
cession of  equivalent  propositions  from  the  most  complex  to 
the  most  simple  form.  Geometry  adopts  the  synthetic  me- 
thod, which  begins  at  the  simplest  elements,  and  proceeds 
to  the  most  complex  combinations :  moreover  it  seizes  upon 
the  matter  and  forms  of  extension  in  their  natural  state,  or 
represents  them  exactly  in  miniature,  making  the  relations 


16 

subsisting  between  lines  and  angles,  superficies  and  solids, 
familiar  to  the  senses,  which  the  algebraic  symbols  cannot 
do,  from  their  position  and  other  obvious  properties  and  ac- 
cidents. In  like  manner  is  algebra,  with  all  its  facilities  of 
substitution,  transposition,  and  elimination,  dependent  in 
its  application  on  a  previous  knowledge  of  arithmetic :  for 
it  must  employ  the  algorithm  of  numbers ;  and  since  every 
number  is  a  term  of  some  series,  the  relations  of  the  given 
numbers  must  be  understood  from  the  law  of  the  series  to 
which  they  belong,  and  from  their  position  in  that  series, 
before  any  advantage  can  be  gained,  either  in  the  demon- 
stration of  a  theorem,  or  the  solution  of  a  problem,  by  means 
of  symbolical  representations. 

For  these  reasons,  we  shall  set  forth,  in  the  leading  num- 
bers of  our  magazine,  the  elements  of  geometry  and  arith- 
metic ;  and  shall  not  attempt  to  generalize  or  concentrate 
propositions  too  hastily,  lest  we  might  defeat  our  most  cher- 
ished hope,  viz :  that  of  enlisting  in  the  cause  of  science  the 
greatest  possible  number.  Our  object  is  to  diffuse  this 
knowledge  where  it  is  most  wanted ;  and  there  is  no  greater 
obstacle  to  this  diffusion  than  the  formulae  of  algebra  ap- 
plied to  principles  not  clearly  understood.  This  doctrine 
is  urged  by  Sir  Isaac  Newton,  and  his  great  preceptor,  the 
learned  Doctor  Barrow,  who  deprecated  in  this  pursuit  noth- 
ing else  so  much  as  the  too  early  application  of  the  analytic 
method,  which  is  chiefly  introduced  with  the  use  of  alge- 
bra. There  is  in  algebra  no  elementary  principle :  why, 
then,  should  it  precede  those  studies  upon  the  principles  of 
which  it  seeks  to  be  engrafted?  Can  the  proportions  of 
numbers  or  the  relations  of  magnitudes  be  at  all  understood, 
when  expressed  only  by  the  letters  of  the  alphabet,  which 
have  not  now,  as  anciently,  a  definite  numerical  value  assign- 
ed to  them?  The  supposition  is  preposterous.  In  short,  a  con- 
tracted and  obscure  view  of  the  uses  of  mathematical  know- 
ledge has  been  superinduced  by  the  early  application  of 
literal  arithmetic  and  the  neglect  of  geometry :  hence  this 


17 

latter  subject  is  scarcely  at  all  estimated  in  the  plan  of  the 
popular  education  ;  the  seeds  of  knowledge  are  withheld 
from  the  youthful  and  vigorous  soil,  by  the  malign  influ- 
ence of  inveterate  habit,  which  clings  to  restrictive  and  dis- 
criminating rules  in  the  diffusion  of  knowledge,  even  in 
cases  where  the  means  are  freely  and  amply  provided. 

It  is  not  our  intention,  however,  to  decry  algebra,  or  to 
dispense  with  the  facilities  which  it  affords  as  the  great 
auxiliary  of  science.  On  the  contrary,  we  shall,  in  the  prose- 
cution of  this  work,  pursuing  our  research  into  the  latitudes 
and  longitudes,  the  depths  and  sublimities  of  Nature's  laws, 
and  their  best  imitation  in  the  works  of  art,  avail  ourselves 
of  all  the  aids  derivable  from  method^  whether  of  composi- 
tion or  resolution  ;  we  shall  not  omit  nor  overlook  the  inter- 
ests of  the  practical  mechanic,  or  the  man  of  science;  but 
shall  introduce,  successively,  with  proper  regard  to  the  nat- 
ural order  and  mutual  dependence  of  the  sciences,  those 
branches  or  parts  of  the  mathematics  which  are  most  pro- 
motive of  public  utility. 

The  Magazine  should  explain  the  terms  which  involve 
principles  in  arithmetic  as  icell  as  in  geometry. — In  the 
arithmetical  department,  it  will  be  deemed  expedient  to 
define  certain  words,  for  the  sake  of  the  principles  with 
which  they  are  connected,  and  to  familiarize  our  junior 
readers  with  the  particular  views  under  which  these  ele- 
ments are  to  be  presented.  A  variety  of  facts  relative  to  the 
doctrines  of  numbers  will  be  collected  under  this  head, 
which  may  occasion  some  appearance  of  delay ;  but,  as  in 
the  clearing  of  a  forest  for  cultivation,  many  difliculties  will 
be  thus  removed,  and  time  and  labor  saved  in  the  general 
result.  In  the  list  of  definitions  the  words  will  be  placed 
in  alphabetical  order,  for  the  convenience  of  reference ;  and 
it  may  be  necessary  to  refer  to  several  words,  in  order  to  un- 
derstand the  principle  to  be  explained,  as  the  words  give  a 
mutual  explication  of  each  other,  and  one  illustration  sheds 
its  hght  upon  another. 


18 

An  explanation  of  the  true  frinciples  of  induction^  as  appU- 
cable  to  arithmetic. — The  organization  of  units  into  series^ 
in  the  formation  of  numbers,  as  the  fundamental  law,  has 
not  been  regarded  by  writers  on  arithmetic  in  the  full  ex- 
tent of  its  importance ;  and  the  effects  of  secondary  causes 
have  been  substituted  in  its  stead.  Hence  the  light  has 
fallen  obliquely,  and  by  reflection,  upon  many  useful  prin- 
ciples, and  errors  have  been  interwoven  with  the  truths  of 
science  in  the  protracted  shades. 

Arithmetic  is  the  science  of  the  numerical  series.  This 
is  its  true  definition ;  and  it  will  be  found  useful  to  con- 
sider the  series  of  cardinal,  ordinal,  multiplicative,  and 
distributive  numbers,  as  in  grammar.  We  shall  here 
notice,  however,  only  the  series  of  cardinal  numbers,  or 
the  numerators  of  things.  In  whatever  way  a  relation  may 
occur  between  required  and  given  numbers,  that  relation 
must  be  investigated  along  the  line  of  some  series.  And  it 
may  be  remarked  that  all  series  consist  of  consecutive  sums, 
differences,  products,  or  quotients ;  since  these  include  all  the 
operations  of  numbers.  The  series  of  numbers  may  all  be 
ranged  into  two  principal  divisions :  first,  the  regular,  which 
have  their  terms  increased  or  decreased  by  a  constant  equal 
quantity ;  and,  second,  the  irregular,  whose  terms  are  in  like 
manner  affected  by  a  variable  quantity.  Each  of  these 
divisions  may  also  be  subdivided  into  classes :  and  of  the 
regular  division,  the  class  of  series  which  have  their  terms 
equi-different  are  called  arithmetical;  and  the  class  whose 
terms  are  continued  proportionals,  ere  called  geometrical. 
Again :  of  the  irregular  division  are  all  additions  and  sub- 
tractions of  simple  numbers,  where  the  result  is  pursued, 
as  it  were,  by  placing  the  given  terms  consecutively  along 
the  line  of  the  natural  series ;  also  the  series  of  triangular 
numbers,  which,  for  several  years,  under  the  name  of  lot- 
teries, has  been  the  medium  of  the  most  frightful  system  of 
deception  and  furtive  traffic,  with  the  sanction  of  ignorant 
or  iaterested  rulers,  and  supported  by  the  cloying  cozenage 


19 

K)Ta  venal  press.  To  digress  a  little  into  the  history  of  this 
case,  it  may  be  remarked,  as  a  very  probable  circumstance, 
that  the  much  boasted  plethora  of  a  certain  State  treasury  is 
occasioned  by  the  revenue  derived  from  the  neighboring 
•cities  by  the  sale  of  lottery  tickets ;  from  which  delusive 
and  criminal  traffic  the  unhappy  adventurers  can  realize 
no  other  issue  than  a  succession  of  disappointments. 

But  to  return  to  our  subject:  To  the  irregular  division 
belong  all  the  series  of  squared,  cubic,  and  pyramidal  num- 
bers ;  and  those  series  whose  terms  consist  of  two  or  three 
unequal  dimensions,  as  in  the  piling  of  balls,  <fcc.  In  this 
division  are  also  the  series  of  powers  and  roots ;  but  the  log- 
arithmic series  of  indices  or  exponents  is  arithmetical,  and 
belongs  to  the  regular  division.  Of  each  division  and  class 
there  is  also  an  infinite  variety  of  series,  and  the  natural 
series  contains  the  terms  of  every  other.  The  decimsd 
terms  1,  10,  100,  1000,  &c.,or  their  multiples,  as  high  as 
the  ninth  inclusive,  in  reversed  order,  constitute  the  organic 
law  of  the  notation  of  numbers;  and,  lastly,  every  series 
has  its  own  measuring  unit,  to  which  every  unit  of  that 
series  must  be  equal  in  dimensions  and  value. 

In  view  of  all  which,  it  is  obvious  that  the  compilers  of 
systems  of  arithmetic  have  not  assumed  the  true  principle 
of  the  science,  either  in  their  definitions,  rules,  or  exempli- 
fications ;  that  they  have  marked  out  no  certain  path  to  its 
perfection ;  and,  consequently,  that  the  progress  of  their  fol- 
lowers is  caliginous  and  erratic.  In  this  consequence,  the 
editors  who  have  professed  to  favor  the  inductive  system  are 
also  involved,  because  they  have  given  no  evidence  what- 
ever that  they  have  made  the  discovery  of  the  general 
law  into  ichich  leads  induction. 

Ttie  leading  numbers  of  the  Magazine  should  not  contain 
abstruse  questions, — This  magazine  will  contain  a  complete 
course  of  mathematics,  and  be  rendered  subservient  to  the 
purposes  of  education  in  families ;  aiding  adults  in  revis- 
ing their  former  studies,  which  may  have  been  passed  over 


20 

too  superficially ;  and  juniors,  by  a  collocation  of  questions, 
under  appropriate  heads,  in  mercantile  and  mechanical  arith- 
metic, adapted  to  the  most  ordinary  capacities,  and  refer- 
red to  the  proper  series  in  every  instance  ;  so  that,  among 
the  earliest  lessons,  the  laws  of  the  several  classes  of  series 
which  form  the  basis  of  all  the  modern  improvements  in 
the  mathematics  will  be  made  familiar  to  the  reader.  The 
object  of  this  publication  will  preclude,  at  the  first,  those 
abstruse  investigations  in  which  the  sons  of  science  delight 
to  exhibit  their  skill ;  and  no  question  can  be  admitted  into 
its  pages  in  anticipation  of  the  principles  upon  which  such 
question  is  founded.  We  intend  to  instruct,  not  to  puzzle 
our  young  readers.  Our  first  numbers  will  be  devoted  to 
the  elements  of  science,  for  the  use  of  that  large  majority  of 
'ci,tizens  who  want  "  the  appliances  and  means'' of  improve- 
ment. It  required  strength  to  bend  the  bow  of  Ulysses,  and 
detailed  practice  to  perform  the  problem  of  the  arrow  gind 
ten  rings;  so  skill  in,  and  power  over,  the  elements  of 
science  accumulate  by  continued  acquisitions. 

Geometry  is  at  war  with  the  lawless  condition  of  mind  and 
Tnatter. — The  elements  of  the  exact  sciences  cannot  be  treat- 
ed in  a  discursive  or  amusing  manner;  on  the  contrary,  the 
random  of  fancy  is  to  be  arrested,  sophistical  arguments  are 
to  be  avoided,  and  the  mental  faculties  required  to  submit  to 
the  impression  of  truth  unmixed  with  error.  Geornetry  deals 
in  realities,  rests  on  admitted  principles ;  and  its  process  of 
investigation  is  the  test  of  philosophical  truth.  But  when 
these  principles  are  duly  cultivated,  they  afford  the  most 
ample  means  of  rational  amusement ;  proving  that  reality  is 
more  astonishing  than  fiction,  because  the  diversified  opera- 
tions of  Nature  are  more  in  number,  beauty,  and  splendor, 
than  the  wild  imagery  of  the  most  fruitful  fancy,  and  the 
discoveries  of  science  excel  all  the  painted  scenery  of  poetry 
and  romance.  Therefore  the  votary  of  science  is  amply  re- 
warded for  the  time  and  pains  expended  in  acquiring  the 
radiments  of  this  knowledge,  which  has  to  contend  for  its 


^1 

v>ery  existence  against  the  gayer  allurements  of  the  spume, 
and  the  unprincipled  drowsiness  oi  X\iQ  sediment  ihdX  mingle 
too  freely  with  the  better  elements  in  the  composition  of 
the  world. 

The  investigations  of  the  sciences  dependent  on  geometry 
are  limited  within  the  knoion  parts  of  the  creation.  The 
line  and  plummet  must  never  be  out  of  use. — The  sublimest 
effort  of  these  studies  is  to  trace  upon  the  tablet  of  the 
human  understanding  a  copy  of  the  plan  of  the  creation, 
the  temple  of  the  Deity  ;  and  to  demonstrate  the  action 
of  its  laws  from  the  partial  view  of  them  attainable  in 
this  remote  position  in  the  solar  system.  They  do  not 
carry  us  out  of  the  limits  of  God's  works  beyond  the  region 
of  light — extra  fiammantia  mcenia  mundi  ;  nor  place  us  an- 
terior to  the  existence  of  time  and  the  motion  of  bodies, 
when  space  alone  existed :  because,  in  the  contemplation 
oi  empty  space,  there  is  no  point  with  which  to  compare,  no 
principle  of  action  or  motion,  and  consequently  no  notion 
of  life  and  its  concomitant  enjoyments;  therefore,  to  date  the 
principles  of  this  knowledge  anterior  to  the  motion  of  bodies, 
except  as  existing  in  the  wisdom  of  the  Deity,  is  an  absurd 
abstraction,  an  ti- geometrical,  a  mere  speculation  of  infidelity, 
which  never  stops  at  the  proper  point,  and,  from  its  morbid 
disaffection  to  the  Supreme  Ruler  and  his  laws,  runs  into 
all  those  absurd  extremes  to  which  geometry  accords  the 
most  consummate  reprobation. 

From  the  motions  of  the  upper  worlds  the  sciences  de- 
scend to  examine  the  contrivances  of  art,  and  to  teach  man- 
kind, from  the  combination  of  a  few  simple  principles  dis- 
covered in  matter,  to  exert  incredible  force  and  ingenuity 
in  the  production  of  the  most  useful  ends.  These  subjects 
will  claim  our  future  attention ;  and  having  access  to  the 
Library  of  Congress,  the  Patent  Office,  and  other  sources  of 
information,  it  will  be  our  aim  to  select  such  materials  as 
shall  be  deemed  most  profitable  to  our  readers,  in  accordance 
with  our  intended  plan  of  conjoining  theory  with  applica- 


22 

tion,  and  of  ascending  the  hill  of  science,  as  the  guide  of  a' 
multitude  of  our  junior  co temporaries,  by  easy,  that  is,  hy 
regularly  graduated  steps. 

The  popular  education  is  defective  with  regard  to  means. 
— Means  are  wanted  to  supply  the  defect,  as  far  as  possible,, 
in  the  popular  education.  There  are,  it  is  ascertained,  about 
one  hundred  colleges  in  the  United  States ;  and  in  these  a 
number  of  students  somewhat  short  of  ten  thousand  are  re- 
ceiving instruction.  It  may  also  be  inferred,  from  the  late 
census,  that  near  three  millions  of  persons  are  of  the  proper 
age  for  instruction  in  schools.  Deducting  the  ten  thousand 
students  from  three  millions,  there  will  remain  two  millioa 
nine  hundred  and  ninety  thousand.  This  immense  majority 
derive  no  direct  advantage  from  colleges,  and  very  little  in- 
directly; because  graduates  of  this  order  generally  have 
higher  pretensions  than  that  of  the  humble  office  of  com- 
mon-school teacher. 

Let  us  inquire,  next,  whether  the  principal  academies  will 
make  amends  for  the  want  of  college  assistance :  of  these 
there  may  be  six  hundred  in  all  the  States,  giving  instruc- 
tion to  sixty  thousand  pupils ;  which,  deducted  from  the 
last  remainder,  will  still  leave  two  million  nine  hundred  and 
thirty  thousand,  who  either  receive  no  instruction  whatever, 
or  so  limited  a  share  of  it  as  to  leave  them  unqualified  for 
the  duties  of  statesmen,  legislators,  judges,  magistrates,  cler- 
gymen, physicians,  lawyers,  military  or  naval  officers,  navi- 
gators, or  even  masters  in  any  of  the  subordinate  trades  and 
professions.  Yet,  from  this  overwhelming  majority  of  un- 
qualified citizens,  the  several  offices  above  mentioned  must 
be  supplied  y  or,  at  least,  they  are  to  be  the  judges  who  will 
determine  as  to  the  qualifications  of  those  who  are  to  fill* 
them. 

An  uneducated  population  are  the  materials  of  a  despotism. 
— Now,  one  of  two  destinies  awaits  our  form  of  government: 
either  it  shall  become  a  despotism,  or  one  of  progressive  so- 
cial improvement;  dependent,  in  the  latter  case^  on  the  gea- 


23 

«ral  and  more  equal  diffusion  of  knowledge.  The  materials 
of  a  despotic  government  are  the  millions  whose  education 
is  so  far  neglected  as  to  eradicate  their  sense  of  equality, 
who,  losing  sight  of  the  first  general  maxim  in  the  Declara- 
tion of  Independence,  are  ready  to  admit  that  they  are  a  sub- 
ordinate class,  and  who  look  to  no  alternative  but  a  change 
of  masters.  The  population  here  described,  whose  individ- 
ual ambition  can  avail  them  nothing,  havCv  nevertheless 
a  powerful  collective  ambition;  though  they  are  undis- 
ciplined in  the  laws,  regard  their  operation  as  partial,  and 
abhor  their  perplexity,  yet  they  have  patriotism,  swell  at 
the  recital  of  their  country's  glory,  and  never  forget  the 
name  of  a  successful  warrior.  They  undervalue  civil  ac- 
quirements, the  operations  of  which  have  no  sensible  effect; 
but  they  are  all  eye,  all  ear,  all  heart,  to  the  tumult  and  os- 
tentation of  war.  The  consequences  of  their  united  action 
may  be  these, — that  the  chieftain  who  shall  lead  them  out  to 
repel  their  country's  invaders  may  probably  lead  them  in  to 
remodel  the  government  more  agreeably  to  his  will.  The 
machine  will  be  found  too  complex  for  the  general  and  his 
followers,  and  they  will  reduce  it  to  the  simple  form  of  a 
general  order.  The  eye  of  such  a  populace  rests  upon  the 
executive,  not  upon  the  laws. 

Domestic  education  is  the  most  available. — Such  are  the 
results  which  must  necessarily  arise  from  the  neglect  of 
the  popular  education;  and  these  results,  which  every 
good  citizen  must  earnestly  deprecate,  are  not  so  remote 
in  the  long  vista  of  ages  as  we  may  supinely  think ;  the 
means  of  prevention  cannot  therefore  be  safely  delayed. 
The  means  of  discipline  in  useful  knowledge,  to  meet 
the  exigence  of  the  case,  must  be  sent  home  to  the  resi- 
dence of  every  citizen,  to  the  farm  and  shop,  where  labor 
and  study  may  relieve  each  other,  and  the  common  mind 
be  enlightened  with  science  at  the  least  expense  either  of 
the  endearments  which  sweeten  the  springs  of  domestic  fe- 
licity, or  of  the  necessary  labor  of  the  people  and  their  pecu- 


24 

niary  means.  They  have  neither  means  nor  opportunities 
to  acquire  the  proper  culture  at  remote  and  higher  institu- 
tions. 

Equal  means  of  education  are  necessary  to  preserve  a  free 
government^  and  avarice  is  its  antagonist. — There  are,  as 
we  have  remarked,  three  millions  of  persons  in  the  United 
States  who  should  be  receiving  instruction  sufficient  to 
qualify  them  for  any  office  in  the  people's  gift.  Seventy 
thousand  of  these  derive  the  form  of  a  liberal  education 
from  colleges  and  higher  schools,  and  two  million  nine 
hundred  and  thirty  thousand  are  comparatively  neglect- 
ed. But  who  will  undertake  to  affirm  that  these,  the  lat 
ter  class,  are  less  endowed  with  natural  intellect  than  the 
former? — or  that,  in  their  business  through  life,  they  less 
require  the  aids  of  literature  and  science  ?  The  defect  of 
equal  and  general  means  for  the  education  of  d^  free  people, 
is  thus  obvious  to  the  least  penetrating  observer.  And  this 
defect  tends  to  create  different  orders  in  the  community ; 
to  be  maintained  for  a  time  by  art,  but  finally  by  an  armed 
aristocracy,  as  in  Mexico,  against  the  common  rights  of  the 
people,  and  the  provisions  of  our  excellent  constitution.  It 
is,  however,  contended  that  education  makes  men  more 
vicious.  That  must  be  a  bad  education,  for  which  we  have 
no  desire  to  provide ;  and  we  also  admit  that  the  disparity 
of  a  good  education  leaves  a  portion  of  the  citizens  unpro- 
tected. But  the  argument  against  education,  whatever  it  is 
worth,  is  drawn  from  an  equality  of  ignorance ;  and  we  aver 
that  the  equality  of  intelligence  will  ever  have  the  same 
claim  to  innocence.  Besides,  intelligence  is  the  characteris- 
tic of  freedom,  of  which  the  United  States  furnishes  con- 
clusive proof.  Education  should  be  of  that  kind  that  resists 
the  commonest  and  most  pernicious  vices.  Now,  avarice 
is  the  first  vice  of  this  and  every  other  commercial  people. 
The  present  generation  are  suffering  the  inevitable  con- 
sequences of  this  passion,  which  is  antagonist  to  a  com- 
monwealth, and  which  was  unknown  to  the  fathers  of  the 


25 

republic.  The  accumulation  of  great  wealth  is  a  very 
ambiguous  test  of  virtue,  and  one  with  which  the  people  are 
never  so  well  satisfied  as  the  security  of  the  possessor 
might  require.  Hence,  the  throes  of  the  country :  hence 
the  strong  effort  of  our  institutions  to  defecate  the  impure 
principles  which  have  aimed  at  their  subversion.  Let  go 
your  ill-acquired  gains,  increase  the  amount  of  productive 
labor,  and  educate  men  to  moderation,  and  all  will  be  well. 
It  is  commonly  charged  upon  the  profligate  and  the  idle, 
that  though  property  were  for  once  equally  divided,  another 
division,  and  anotlier,  would  be  necessary  to  preserve  the 
equality.  But  this  consequence  is  produced  by  the  cove- 
tous man  rather  than  the  spendthrift.  The  latter  relaxes  his 
grasp  upon  his  property,  and  the  former  snatches  it  out  of 
his  hand.  One  is  generous  and  unsuspecting,  the  other  is 
subtle  and  rapacious.  One  would  permit  a  portion  of  the 
public  property  to  be  in  common,  the  other  appropriates  to 
his  own  use  every  thing  which  he  is  able  to  seize.  If  all 
the  wealth  which  can  be  acquired  from  the  imbecility  of 
others,  or  through  the  error  of  legislation,  be  justly  yours, 
why  not  at  once  return  to  the  old  doctrine,  that  might  is 
right? 

Legislation  requires  intellectual  discipline  and  experience 
of  the  relations  of  society. — We  would,  However,  insist  on 
the  necessary  qualification  in  our  rulers  :  we  say,  they  ought 
to  be  educated  men.  It  is  our  intention  to  excite  emulation, 
not  envy.  Let  us  examine  societ^n  its  formation :  it  is  the 
natural  condition  of  man.  The  writers  on  international 
law,  to  form  some  basis  for  an  argument,  have  supposed 
cases  of  solitude  which  have  never  existed.  To  talk  of 
rights  in  the  case  of  one  who  has  abandoned  all  his  rights, 
and  can  suffer  no  wrongs,  unless  those  which  he  may  inflict 
on  himself  in  his  gloomy  forest  cave,  is  one  of  the  ex- 
travagancies of  infidelity  for  which  some  of  these  popular 
writers  are  remarkable.  Man  came  into  society  when  he 
came  into  existence:  all  men  are  born  equally  helpless; 


26 

they  have  a  right  to  life,  for  the  same  reason  that  society- 
has  a  right  to  exist;  and,  for  any  thing  that  appears  in 
evidence  in  the  matter,  one  is  as  well  entitled  to  liberty 
and  the  pursuit  of  happiness  as  another — id  est,  liberty  to 
seek  or  pursue  his  happiness ; — which  happiness  consists 
in  the  enjoyment  of  that  temperature  of  mind  that  is  ef- 
fected by  the  unresisted  action  of  the  law  of  his  being. 
The  Creator  has  willed  man's  happiness,  but  the  means 
are  not  acquiesced  in:  hence  society  requires  to  be  con- 
nected and  secured  by  sanitary  regulations.  The  mem- 
bers of  society  are  dependent  on  each  other;  the  whole 
body  is  dependent  on  the  Great  Original  Existence.  The 
machine  is  a  complicated  one,  and  its  laws  must  be  in 
some  measure  understood  by  the  man  whom  we  could  con- 
scientiously recommend  to  one  of  its  responsible  offices. 
Therefore,  we  aver  that  legislators,  judges,  and  executive 
officers  should  understand  the  structure  of  the  body  politic, 
and  also  the  rights  and  moral  obligations  of  the  whole,  as 
well  as  the  several  parts.  In  short,  every  human  enactment 
ought  to  assume  to  be  nothing  more  than  a  simple  declara- 
tion of  some  inference  deducible  from  that  general  rule,  by 
the  observance  of  which  the  happiness  of  the  whole  and  of 
the  parts  is  promoted. 

For  such  reasons  as  these  we  would  rather  see  men  hold- 
ing responsible  offices  who  have  undergone  a  course  of 
mental  discipline ;  but  we  wish  all,  or  a  sufficient  majority, 
as  many  as  possible,  to  He  eligible ;  therefore  we  desire  to 
let  out  the  streams  of  science  upon  this  national  husbandry 
in  every  possible  direction.  The  available  media  for  the 
diffusion  of  knowledge,  now  in  existence,  are  the  colleges, 
academies,  and  common  schools  ;  of  which  the  number  of 
the  latter  bears  to  that  of  both  the  former  about  the  same 
ratio  as  three  hundred  to  one. 

Concentration  and  diffusion  of  knowledge  contrasted, — 
The  concentration  and  the  diffusion  of  knowledge  may 
be  contrasted.    High  and  expensive  institutions  tend  to  the 


27 

foraier  rather  than  the  latter ;  the  seeds  of  knowledge,  like 
those  of  plants,  must  be  disseminated  upon  the  broad  basis, 
not  grudgingly,  but  with  a  generous  hand ;  we  may  add, 
after  the  manner  of  Christianity.  The  same  may  be  said  of 
eminent  works  of  science.  To  the  Principia  of  Newton,  per- 
haps, no  well-adapted  additions  could  be  made;  but  the 
general  diffusion  of  this  colossal  knowledge  requires  means 
different  from  any  that  have  been  hitherto  employed ;  and 
so  likewise  of  geometry  and  other  natural  sciences.  Col- 
leges and  academies  are  too  expensive  to  be  placed  at  all 
points  ;  it  follows,  therefore,  that  the  common  schools  of  the 
country  are  the  proper  media  for  the  diffusion  of  knowledge. 
But  it  may  be  seiid  that  these  are  already  effecting  the  ob- 
ject contemplated  in  their  establishment.  This  may  indeed 
be  true  in  numerous  cases ;  but  the  object  so  contemplated 
may  not  be  commensurate  with  the  increasing  necessity  of 
knowledge.  We  have  known  certain  schools  which  have 
been  supported  liberally,  at  public  expense,  for  a  quarter  of 
a  century,  in  which  the  progress  of  science  has  been  stopped 
at  the  point  which  they  technically  call  the  rule  of  three. 
This  may  have  been  the  contemplated  limit  of  the  object 
for  which  such  schools  were  established ;  and  the  practice 
has  corresponded  to  the  design.  But  such  restriction  is  evi- 
dently incompatible  with  the  march  of  mind,  as  well  as 
with  the  natural  fecundity  of  the  mental  soil.  Was  this  the 
proper  method  to  neutralize  the  superior  advantages  of  col- 
legiate instruction,  and  equalize  the  acquirements  of  the 
citizens  in  knowledge  and  power?  Certainly  not.  The 
case  alluded  to  may,  perhaps,  be  of  rare  occurrence,  repre- 
senting common  schools  in  their  least  efficient  state. 

The  metaphorical  tree  of  knowledge. — The  tree  of  knowl- 
edge is  a  familiar  figure  of  speech ;  and  the  departments 
of  science  are  so  commonly  denominated  branches^  that 
this  term  is  scarcely  regarded  as  a  metaphor,  but  rather 
as  a  literal  expression.  It  would,  however,  be  no  disad- 
vantage to  the  cause  if  the  figure  were  carried  out  more 


28 

extensively,  so  as  to  embrace  the  trunk,  juices,  and  fruit; 
also  the  condition  of  the  tree,  whether  as  a  stunted  shrub 
or  a  stately  fruit-bearer.  This  would  afford  a  basis  for  a 
more  vivid  illustration  of  the  minute  origin,  connexion, 
dependence,  and  progress  of  the  elements  ;  showing,  from 
the  nature  of  the  fruit,  branches,  &c.,  that  the  seed  is  of  two 
kinds — number  and  extension ;  that  with  number  alone,  only 
a  stunted  shrub  is  produced  ;  that  although  the  larger  and 
smaller  branches  of  the  stately  tree  partake  of  the  properties 
of  numbers,  yet  those  of  extension  are  so  interwoven  in  the 
entire  texture  as  to  preclude  access  to  the  fruit  by  the  skill 
and  power  of  numbers  alone ;  that  the  season  of  planting 
and  culture  ought  not  to  be  neglected,  and  that  the  soil 
ought  to  be  duly  selected  and  prepared. 

The  elements  of  science  are  not  acquired  at  the  proper 
season,  and  therefore  rarely  ever.  Their  light  is  hid  as  under 
a  bushel  ijBom  the  mass  of  the  people ;  or,  to  use  a  continen- 
tal simile,  the  channel  of  their  mighty  river  is  closed  by  the 
sunken  rafts  of  time-honored  erudition,  and  the  deep  current 
passes  off  on  the  sinister  hand,  for  the  exclusive  benefit  of 
a  very  limited  number.  Even  in  the  best  institutions  the 
quantity  of  this  knowledge  is  abated,  from  the  want  of  appro- 
priate means  of  acquiring  it  in  the  preparatory  schools. 

School  commissioners  and  trustees  are  bound  to  lay  a  pro- 
per foundation  for  p^iblic  instruction. — To  incorporate  the 
elements  of  geometry  with  the  popular  education  is  an 
indispensable  duty,  binding  upon  those  who  are  intrusted, 
by  commission  or  otherwise,  with  the  direction  of  this 
important  branch  of  public  affairs.  Let  your  pupils  read 
and  become  familiar  with  Euclid's  propositions  and  dia- 
grams at  the  proper  age,  before  the  opportunity  is  snatched 
away  from  them  by  procrastination.  Consider  the  results 
in  the  cases  of  Newton  and  Bowditch,  and  a  thousand 
others  of  merely  accidental  opportunities  of  reading  works 
of  science.  The  former  of  these  great  men  was  not  in- 
tended for  a  liberal  scholar :  he  was  employed  as  a  helper 


29 

on  his  mother's  farm,  when  Euclid's  Elements  fell  into 
his  hands :  he  understood  the  propositions  of  that  author 
by  simply  reading  them ;  they  presented  to  his  capacious 
mind  no  difficulty ;  and  from  such  powerful  manifestation 
of  intellect  was  drawn  the  motive  for  sending  him  to  the 
university.  He  lived  to  express  his  regret  that  he  had  occu- 
pied so  much  time  upon  the  theories  of  Des  Cartes,  and  that 
he  did  not  limit  his  investigations  within  the  range  of  the 
principles  of  Euclid's  Elements,  as  being  the  most  direct 
way  to  his  own  discoveries.  Doctor  Nathaniel  Bowditch, 
it  is  well  known,  collected  the  seeds  of  science,  by  which 
he  has  done  honor  to  his  country,  and  established  for  him- 
self an  imperishable  name,  from  some  volumes  which  he 
found  in  the  ship-chandler's  office  where  he  was  employ- 
ed. Give  to  the  rising  generation  the  means  of  perusing 
the  elements  of  geometry, — this  is  the  defective  point  for 
which  there  is  no  equivalent  study, — and  the  next  age  will 
be  illustrious  for  its  Newtons  and  Bowditches.  Then  will 
arise  many  ornaments  of  society  in  this  department  of  knowl- 
edge. After  the  manner  of  Sir  Charles  Scarborough,  they 
will  be  able  to  repeat,  in  order,  all  the  propositions  of 
Euclid,  Archimedes,  and  other  ancient  authors  ;  and,  like 
Sir  Isaac,  comprehend  them  without  the  labor  of  much 
study.  The  eminent  mathematician  above  mentioned  was 
physician  to  Charles  the  Second,  and  his  two  successors,  as- 
sistant and  successor  to  Doctor  Harvey,  as  lecturer  on 
subjects  of  anatomy  and  surgery,  and  the  first  who  judi- 
ciously applied  mathematics  to  medical  subjects. 

A  Chart  and  Manual  of  Geometry  for  the  use  of  schools 
recommended, — In  addition  to  the  magazine  herein  proposed 
to  be  published,  as  one  of  the  incipient  means  of  diffusing  the 
knowledge  of  the  exact  sciences  more  equally  and  generally 
among  the  people,  we  have  devised  a  series  of  charts  of  the 
diagrams  of  geometry,  and  a  manual  of  the  definitions,  pos- 
tulates, axioms,  and  propositions  of  Euclid  to  accompany 
the  charts.     This,  indeed,  is  but  the  seed  of  a  glorious  har- 


30 

vest  of  knowledge — worthy  of  being  so  esteemed,  because  of 
its  general  diffusion ;  and  general,  because  of  its  congeniality 
to  the  operations  of  every  well-regulated  human  mind.  It  is 
our  earnest  wish  to  make  the  impression  of  the  forms  of 
extension  precede  the  work  of  analysis,  and  to  furnish  the 
corresponding  propositions  according  to  the  ancient  and  ap- 
proved order  of  the  Greek  geometer.  Any  deviation  from 
this  arrangement  would  only  open  the  way  for  an  endless 
train  of  pretended  improvements,  which  would  no  more 
subserve  the  purpose  of  general  diffusion  than  the  present 
refinements  of  analysis  are  effecting. 

A  description  of  the  Chart  and  Manual  of  Geometry  <j  ivith 
the  title  of  each^  and  the  supposed  terms  of  their  publica- 
tion.— The  chart  No.  1,  of  the  series  here  alluded  to,  will 
contain  the  diagrams  of  the  six  books  of  Euclid ',  exhibit- 
ing nearly  three  hundred  strong  lined  figures,  on  an  area  of 
twenty  square  feet  of  plate  paper  laid  on  cloth,  with  mould- 
ing and  roller,  bound  and  varnished  in  the  manner  of  a  map ; 
or,  as  it  will  consist  of  four  equal  plates,  if  required,  it 
may  be  so  mounted  as  to  fold  in  quadruple,  without  the 
wood,  for  the  purpose  of  transportation.  The  manual 
No.  1  will  contain  the  definitions,  axioms,  postulates,  and 
propositions  of  the  same  books,  wanting  the  demonstra- 
tions. The  rules  for  constructing  the  figures  will,  however, 
be  given;  also  the  references  to  the  elements  preceding 
each,  usually  quoted  as  proofs. 

1.  The  Chart  of  Geometry,  No.  1,  exhibiting  the  dia- 
grams of  the  first  six  books  of  Euclid :  to  accompany  the 
Manual  of  Geometry,  No.  1,  containing  the  propositions  and 
other  elements  of  the  same  books.     Price,  $5  per  copy. 

2.  The  Manual  of  Geometry,  No.  1,  containing  the  defi- 
nitions, postulates,  axioms,  and  propositions  of  the  first  six 
books  of  Euclid :  to  accompany  the  Chart  of  Geometry, 
No.  1,  exhibiting  the  diagrams  of  the  same  books.  Price, 
not  exceeding  $3  per  dozen.  But  each  copy  of  the  chart 
will  be  entitled  to  one  copy  of  the  Manual  without  extra 
charge. 


31 

It  will  be  recollected  that,  wherever  geometry  is  taught, 
the  figures  are  commonly  drawn  on  a  blackboard,  and  ef- 
feced  with  the  occzision ;  losing  thus  the  advantage  deri- 
vable from  subsequent  reference.  If  this  practice  should 
still  be  continued  in  connexion  with  the  chart,  the  latter 
will  serve  as  a  record  of  such  transactions,  and  be  a  use- 
ful auxiliary  in  the  college  hall,  as  well  as  a  pioneer  in  the 
preparatory  school. 

Geometry  and  arithmetic  should  be  taught  at  (he  same 
time. — It  is  susceptible  of  the  most  satisfactory  demonstra- 
tion that  arithmetic  and  geometry  should  be  simultaneous 
studies  ;  it  is  also  well  known  that  the  want  of  a  practicable 
plan,  alone,  has  in  many  instances  prevented  this  union. 
It  is  proper,  however,  to  remark,  that  the  former  requires 
the  aid  of  the  latter,  rather  than  the  contrary.  Geometry 
depends  for  the  proof  of  its  propositions  upon  its  own  ele- 
ments; whereas  arithmetic  requires  the  extended  dimen- 
sions of  geometry  to  illustrate  the  principles  of  its  opera- 
tions :  this  will  apply,  however,  to  the  case  of  rectilineal 
figures.  In  the  theories  respecting  curves,  the  excellence 
of  Newton's  demonstrations  consists  in  his  superlucid  ap- 
plication of  the  doctrine  of  infinite  series,  in  which  geom- 
etry requires  the  aid  of  numbers ;  in  the  mixed  mathe- 
matics, they  are  professedly  subservient  to  each  other. 

The  entire  labor  of  demonstration  should  not  be  at  once 
imposed  on  the  learner. — It  is  reduced  to  a  maxim,  that  the 
classification  of  labor  facilitates  its  performance.  The  plan 
here  proposed  is  to  omit  the  demonstrations,  but  not  any  of 
the  elementary  principles,  in  the  commencement  of  this 
study.  The  first  care  of  the  learner  should  be  to  know  each 
proposition  in  order ;  its  data,  or  given  parts ;  its  quaesita,  or 
requirements  ;  to  construct  the  corresponding  diagram,  or  at 
least  to  trace  it  out  with  a  pencil,  or  otherwise,  by  its  points, 
lines,  and  angles ;  so  that  it  may  be  clearly  identified  \vith 
the  proposition,  and  the  enunciation  of  the  proposition 
readily  given  from  an  inspection  of  the  diagram.    These 


32 

preliminary  exercises,  which  do  not  fall  far  short  of  the  full 
amount  of  labor  required  in  this  study,  may  be  performed  in 
the  family  circle,  in  schools  of  any  grade,  by  any  person 
who  can  read,  as  well  as  by  a  learned  geometer.  Let  no 
time  be  lost  in  committing  to  memory  the  definitions, 
axioms,  and  postulates,  since  the  constant  reference  to  them, 
at  each  proposition,  will  soon  render  them  familiar;  read 
them,  and  pass  on  to  collect  other  facts. 

Youth  is  the  proper  time  for  acquiring  science,  and  form- 
ing an  intelligent  citize?i. — In  order  to  form  the  young 
mind  to  place  within  it  the  organizing  principles  of  geome- 
try, the  burden  of  this  study  must  be  assumed  in  youth, — 
that  season  of  life  in  which  the  memory  is  susceptible  of 
defined  impressions,  and  most  willingly  submits  to  the  im- 
position of  a  task ;  and  these  elements  must  be  thus  ac- 
quired, or  the  demonstrations  cannot  be  efiected  ;  he  shall 
only  make  the  discovery  of  his  own  impotency  (for  want 
of  knowledge  is  want  of  power)  who  will  undertake  the 
latter  without  the  necessary  preparation.  And  unless  a  man 
possess  the  intuitive  perception  of  the  truths  of  science,  or 
receive  it  by  a  course  of  instruction,  a  morbid  ignorance  and 
hesitating  uncertainty  will  embarrass  all  his  thoughts,  or  a 
precipitate,  turgid,  unwarranted  assurance  will  mark  his 
course  through  life ;  one  unbalanced  passion  will  control 
him ;  he  cannot  be  an  enlightened  citizen  of  this  republic  ; 
he  will  behold  the  improvements  of  art  with  a  vacant  stare, 
and  be  a  helpless  loiterer  in  the  march  of  mind.  The  moral 
influence  of  the  sciences  is  not  duly  appreciated  in  the  af- 
fairs of  this  Government,  dependent  as  it  is  on  the  popular 
will. 

Geometry  taken  in  the  Euclidian  order  is  not  abstruse, 
and  m.ay  be  learned  by  any  good  reader. — If  it  should  be 
objected  that  the  study  of  geometry  requires  maturity  of 
judgment  and  riper  years,  it  may  be  answered  that  the 
mind,  in  this  case,  i^  required  to  create  nothing ;  the  state- 
ments and  proofs  are  all  furnished ;  and  the  principles,  as 


33 

well  as  their  application,  are  as  simple  and  obvious  as  those 
of  grammar  or  geography.  This  latter  branch  is.  indeed, 
a  dependent  on  geometry,  deriving  its  forms  and  propor- 
tions from  it,  having  been  successfully  and  commonly 
taught  in  schools  only  a  few  years, — that  is,  since  the  atlas 
accompanied  the  book  of  descriptions.  And  as  to  gram- 
mar, it  is  comparatively  abstruse  and  metaphysical ;  not  a 
subject  of  form  or  extension,  and  therefore  evading  the 
action  of  the  senses ;  yet  it  has  been  reduced  to  the  ca- 
pacity of  juvenile  learners,  and  made  a  common  study 
in  all  the  schools.  Geometry,  taken  in  the  Euclidian  order, 
is  easy  and  natural;  an  isolated  problem,  depending  on 
principles  wholly  unknown  to  the  performer,  (and  this 
is  what  we  propose  to  provide  against,)  presents  an  insur- 
mountable barrier  to  the  tallest  intellect ;  like  the  elevating 
of  a  block  of  marble  upon  a  lofty  column,  which  cannot  be 
effected  without  the  intervention  of  the  mechanic  powers  ; 
so  the  difficulties  of  all  such  problems  are  removed  by  a 
previous  acquaintance  with  the  Elements  of  Euclid.  With 
a  due  regard  to  the  progressive  abilities  of  the  learner,  it 
may  be  said  that  he  is  prepared  to  enter  upon  this  study  so 
soon  as  he  can  read  sufficiently  well  to  exercise  his  memory 
on  the  subject  of  his  lection. 

Teachers  may  acquire  this  knowledge  from  the  recitations 
of  their  pupils,  tcithout  any  previous  study. — To  teachers 
unacquainted  with  geometry,  but  who  desire  to  extend 
their  sphere  of  usefulness,  the  plan  here  proposed  presents 
the  most  favorable  opportunity  of  learning  from  the  recita- 
tions of  their  pupils.  The  frequent  rehearsal  of  the  same 
task  through  successive  classes,  with  the  continual  ref- 
erence to  the  diagrams  on  the  chart,  and  to  the  preceding 
proofs  at  each  proposition  in  the  Manual,  cannot  fail  to  give 
the  impression  of  this  knowledge  in  the  shortest  possible 
time.  Many  zealous  and  qualified  laborers  would  thus  enter 
the  fields  of  science  ;  the  laws  of  Nature  would  be  more  fully 
explored,  and  made  the  subjects  of  general  reflection  and 
3 


34 

models  of  action  among  men.  Hence  the  most  beneficial 
results  would  accrue  to  the  community  from  the  regulating 
influence  of  those  perfect  examples  upon  the  ardent  passions 
of  the  young  :  the  moral  as  well  as  the  intellectual  condi- 
tion of  society  would  be  improved,  by  diffusing  the  knowl- 
edge of  Nature's  laws,  of  whose  operation  geometry  is  not 
a  system  of  symbolical  representations,  but  rather  a  min- 
iature likeness. 

Colleges  have  a  pecuniary  interest  in  the  promotion  of  this 
preparatory  study. — Professors  and  teachers  who  have  the 
charge  of  instructing  young  men  in  the  mathematical  de- 
partment in  colleges  and  academies  are  expected  to  sanc- 
tion this  plan,  until  a  better  can  be  provided,  of  inculcating 
an  early  acquaintance  with  geometry.  Here  the  materials 
will  be  prepared  to  some  distance  in  advance  of  the  quali- 
fied demonstrator,  who  will  doubtless  find  the  business  of 
wrangling  not  only  facilitated,  but  greatly  multiplied  on  his 
hands,  by  the  immission  of  eager  applicants  from  the  lower 
schools,  where  the  use  of  the  manual  and  chart  may  be 
adopted.  Men  are  not  apt  to  care  for  that  of  which  they 
know  nothing,  however  good  it  may  be  in  itself;  but  a  par- 
tial insight  into  this  knowledge  will  quicken  a  desire  to 
know  more :  and  there  can  arise  no  rational  fear  that,  in  the 
case  of  the  most  assiduous  student,  during  the  years  usually 
passed  at  college,  the  subject  of  the  mathematical  sciences 
will  be  exhausted. 

Geometry  is  the  law  of  Nature,  as  it  regards  action  or  mo- 
tion.— And  what  is  geometry  ?  let  it  be  asked ;  or  the  study 
which  we  are  endeavoring  to  advocate  ?  To  premise,  in 
answer,  we  remark,  that  the  works  of  art  are  imitations,  not 
creations.  It  may  be  truly  asserted  that  in  mechanics  no 
usefiil  discovery  has  ever  been  made,  even  inadvertently, 
unless  where  the  mind  had  been  previously  drawn  out,  with 
or  without  design,  into  that  natural  order  of  thought,  which 
the  association  of  contiguous  objects  and  a  succession  of 
generated  motions  had  suggested  to  it;  and  that  every 


35 

^iseful  invention  is  nothing  more  than  the  development  of 
«ome  natural  law,  although  the  inventor  himself  may  not 
^e  able  to  recollect  the  train  of  reflections  which  conducted 
him  to  his  conclusions.     This  may  serve  to  show  the  wis- 
dom of  investigating  the  causes  and  effects  of  things  in  the 
way  which  Nature's  laws  prescribe,  in  order  that  advantage 
may  be  taken  of  those  irreversible  rules  of  action,  and  a 
helpful  co-operation  instituted  between  nature  and  art.     In 
this  consists  the  truth  of  the  maxim  that  "  knowledge  is 
power."     The  folly  of  opposing  those  rules,  or  dispensing 
with  them,  is  set  forth  in  the  proverbs  of  every  language  of 
which  we  have  any  account ;  and  every  year,  in  the  con- 
duct of  some  one  or  other  who  spends  his  time  and  money 
in  the  fruitless  search  of  a  motive  power  inherent  in  the  yet 
unknown  combinations  of  matter.     The  laws  of  motion  and 
forces  are  here  particularly  alluded  to ;  and  these  pervade 
the  universe.     Every  part  of  the  creation  is  in  motion  ;  air, 
earth,  water,  fire,  light,  heat,  sound,  time,  the  planets, comets ", 
and  it  may  be  (for  the  standard  of  comparison  is  too  great 
for  our  comprehension)  the  whole  solar  system,  all — all  are 
in  motion,  unvarying,  incessant.     To  these  are  analogous? 
the  mechanical  and  chemical  actions  of  the  works  of  art ; 
and  all  are  subject  to  the  rules  of  geometry.     The  study  of 
geometry  is  therefore  an  inquiry  into  Nature's  laws. 

A  few  of  the  many  uses  of  geometry  to  a  free  people  enu- 
merated.— Self-government  is  the  great  business  of  the  peo- 
ple who  would  be  free  :  this  consists  in  a  voluntary  conform- 
ity to  th€  best  natural  and  social  regulations ;  which  implies 
a  knowledge  in  the  people  of  their  rights  and  their  duties, 
their  wants  and  their  means  of  providing  for  them.  To  a 
self-governing  people  every  kind  of  useful  knowledge  is  in- 
dispensable, and  there  is  none  more  prolific  of  utility  than 
geometry.  We  have  already  alluded  to  the  maxim  that 
"knowledge  is  power;"  and  besides  this,  we  have  it  upon 
the  authority  of  holy  writ,  that  "  the  soul  to  be  without 
knowledge  is  not  good."    If,  therefore  ,  the  people  of  the 


United  States  will  preserve  their  two-fold  character  of  rulew 
and  subjects,  and  execute  the  double  function  in  the  best 
manner,  the  range  of  their  popular  education  must^  be  ex- 
tended, and  the  pabulum  mentis^  the  intellectual  nutriment, 
supplied  in  proportion  to  the  growing  wants  of  their  in- 
creasing population.  To  this  end  every  facility  should  be 
given  to  the  diffusion  of  the  useful  arts,  very  many  of  which 
depend  for  their  origin,  progress,  and  perfection,  upon  the 
knowledge  of  geometry.  To  enumerate  all  the  uses  of  this 
science,  would  be  to  evoke  the  practical  operations  of  the 
better  half  of  the  busy  world.  Let  it  suffice  to  say  that  it  is 
eminently  the  science  of  national  defence  by  land  and  sea  -, 
of  strategy  or  the  marshalling  of  troops ;  of  the  motion  of 
projectiles  and  of  gunnery;  of  the  building  of  ships  and 
fortifications ;  of  navigating  the  trackless  ocean,  from  the 
comparison  of  times  and  distances,  marking  the  revolutions 
of  the  stars  and  planets.  Geometry  is  the  science  which 
teaches  the  erection  and  adornment  of  edifices ;  the  construe  - 
tion  of  bridges,  mills,  machines,  and  engines ;  the  distribu- 
tion and  subduing  of  the  glebe ;  the  graduating  and  con- 
ducting of  watercourses  and  railways;  the  surveying  of 
coasts,  shiproads,  and  rivers,  and  marking  the  relative  posi- 
tion of  headlands  and  other  stationary  objects  for  the  gui- 
dance of  the  mariner  in  view  of  land.  Geometry  furnishes 
all  the  principles  for  the  fabrication  of  musical,  optical,  and 
nautical  instruments,  and  the  means  generally  of  exerting 
human  power  successfully  against  the  resistance  of  matter 
in  all  its  forms,  so  as  to  accomplish  with  extreme  precision 
the  minutest  as  well  as  the  most  stupendous  works. 

The  study  of  geometry  produces  internal  order,  regulates 
the  morals,  and  elevates  the  mind  to  contemplate  the  sacred 
order  of  the  Creator^s  works. — Geometry  is  a  moral  science, 
or  in  closer  alliance  with  the  science  of  morals  and  religion 
than  any  other  of  the  physical  sciences.  The  study  of  it 
places  within  the  soul,  as  it  were,  a  framework  of  truth,  on 
which  to  dispose  in  due  order  the  faculties,  affections  and 


37 

passions,  under  the  control  of  reason;  a  trellis  for  the  sup- 
port and  display  of  the  fruits  of  virtuous  principles,  hon- 
orable to  the  student,  and  salutary  to  those  who  are  favored 
with  his  worthy  example.  The  diseases  incident  to  a  col- 
lapsed condition  of  the  moral  powers  find  here  a  remedy ; 
which  powers,  so  arranged,  instead  of  exhausting  their  force 
in  mutual  collision,  severally  act  their  appropriate  functions 
within  their  destined  spheres.  The  mind  is  thus  led,  from 
its  own  internal  order,  to  contemplate  the  sacred  order  of 
the  Creator's  works  ;  to  admire  the  wisdom  of  their  arrange- 
ment and  the  harmony  of  their  several  parts ;  to  exult  in 
deriving  its  own  existence  immediately  from  the  Almighty 
Architect  himself. 

Good  government  is  a  Divine  unity  ;  and  a  freeman  must 
either  exercise  it  upon  himself  or  fall  into  the  hands  of  another 
master. — It  is  not,  however,  pretended,  nor  can  it  be  be- 
lieved, that  good  morals  or  good  government  can  exist  in 
the  absence  of  religion.  Grood  government  is  an  indivisible 
unit,  descending  from  the  Blest  Supreme,  and  apportioned  to 
his  creatures  as  they  can  bear  it.  It  pleases  the  people  of 
the  United  States  to  hold  the  reins  for  themselves,  by  God's 
grace,  not  feignedly  as  usurpers,  but  as  of  duty  under  the 
most  sacred  obligations,  taking  the  ultimate  responsibility, 
or  to  depute  the  task  for  a  time  to  chosen  men,  whose  duty 
it  is  made  to  direct  the  power  of  the  whole  equally  for  the 
good  of  each  individual :  but  where  self-government  is 
vigorous,  external  government  is  the  less  wanted,  and  des- 
potism fails  of  its  object  through  the  want  of  materials  upon 
which  to  act.  But  that  man  is  not  free  who  has  lost  the 
government  of  himself — who  has  broken  loose  from  his 
own  restraint.  The  apostolic  gradation  is  the  theory  of 
perfect  liberty, — faith,  virtue,  knowledge,  temperance,  pa- 
tience, godliness,  brotherly  kindness,  charity  :  these  libera- 
ting operations  are  effected  by  Divine  assistance,  and  not 
otherwise ;  for  we  cannot  know  even  natural  things  in  their 
true  relations,  unaided  by  the  internal  illustrations  of  tlie 


wisdom  which  is  from  above.  Nevertheless,  the  study  oi 
the  natural  sciences  is  here  recommended  in  connexion  with 
that  of  redemption ;  but  all  history  attests  that  the  study  of 
the  mathematics  preponderates  vastly  in  favor  of  true  and 
exalted  piety. 

The  diagrams  and  propositions  of  geometry  should  be 
every  where  exhibited, — If,  therefore,  these  elements  of  the 
natural  sciences  be  of  so  very  great  importance  to  the 
people  of  the  United  States,  why  should  any  rational 
means  of  rendering  them  effective  be  neglected  in  the 
popular  education?  The  public  and  private  service  of  the 
country  calls  for  a  more  general  diffusion  of  this  know- 
ledge. Either,  then,  let  some  better  means  be  devised,  or 
let  this  chart  of  the  diagrams  be  spread  out,  and  this  man- 
ual of  the  propositions  of  Euclid  be  suspended  to  it,  as  the 
farmer  suspends  his  almanac  for  the  service  of  the  year, 
in  every  district  school ;  in  every  mechanic's  shop,  every 
counting-room,  every  public,  society,  or  firemen's  hall, 
where  young  men  resort;  in  the  domicil, among  the  rising 
youth  ;  at  every  military  post  and  naval  station ;  in  the 
quarters  of  midshipmen,  and  petty  officers  and  seamen,  when 
at  sea ;  and,  where  it  might  not  be  an  inappropriate  ap- 
pendage, in  the  libraries  of  young  lawyers,  with  the  Com- 
mentaries of  Blackstone  and  Kent.  Then  will  abler  ad- 
vocates enter  the  forum,  furnished  with  Eu<ilid's  invincible 
style  of  argument  and  the  strong  fulcrum  of  truth,  on 
which  to  rest  a  plea ;  the  wet  seaboy  would  devote  his 
watch  below  to  the  improvement  of  his  nautical  skill;. 
old  soldiers,  among  whom  are  not  often  wanting  those  who 
would  recognise  in  Euclid  a  former  acquaintance,  would 
take  new  delight  in  explaining  to  their  comrades  the  na- 
ture and  application  of  his  diagrams,  reminding  them  of 
the  long  defence  of  Syracuse,  by  the  science  of  Archimedes, 
against  Marcellus,  the  sword  of  Rome ;  the  apprentice 
would  tax  the  leisure  of  his  servitude  with  the  acquisition 
of  this  knowledge,  which  would  qualify  him  to  test  the 


strength,  under  certain  combinations,  and  overcome  the 
resistance  or  resist  the  pressure  of  the  massive  materials 
used  in  the  works  of  art;  and  the  domicil  and  school 
would  send  forth  to  the  halls  of  legislation  orators  more 
succinct  and  cogent,  statesmen  better  informed  respect- 
ing the  nature  of  productive  labor,  the  cost  of  public  works, 
and  the  economical  expenditure  of  the  revenues  of  the 
country. 

Let  the  temperance  associations,  especially,  recommend  it 
to  the  young,  as  a  substitute  for  the  coarse  revelry  with 
which  they  aflfect  to  be  happy.  While  reformed  men,  and 
those  who  have  always  shunned  the  cup,  are  uniting  their 
efforts  in  rooting  up  the  vice  of  inebriety  with  all  its  con- 
comitants, the  soil  which  they  clear  will  not  lie  fallow ;  the 
seeds  of  many  evils  exist  in  the  human  constitution,  ready 
to  spring  forth  in  native  luxuriance,  in  the  absence  of  restrain- 
ing goodness.  The  active  mind  of  man  seeks  employ- 
ment ;  and  inexperience  unfits  it  for  judging  of  that  which  is 
most  profitable.  If  the  elements  of  geometry  be  dissemi- 
nated and  receive  proper  culture,  the  fruit  will  be  perfec- 
tion in  many  of  the  useful  arts,  and  purity  and  power  of 
self-protection  in  the  details  of  our  institutions.  This 
would  produce  a  salutary  action  in  the  body  politic,  and 
prevent  many  of  the  disorders  which  disturb  the  peace  of 
the  community. 

Geometry  is  necessary  to  complete  the  education  of  an 
American  citizen. — It  was  anciently  said  that  there  is  no 
royal  road  to  geometry ;  or,  in  other  words,  no  way  to  under- 
stand the  laws  of  Nature  without  the  labor  of  study :  this  is 
now  a  truism,  as  much  as  it  was  in  the  days  of  Ptolemy.  Here, 
however,  there  is  no  royalty  to  desire  exemption  from  labor  3 
and  freemen  labor  for  themselves ;  also,  in  the  pursuit  of 
knowledge  they  seek  a  treasure  beyond  the  reach  of  fraud. 
But,  as  freemen  labor  for  themselves,  so  they  govern  them- 
selves ;  they  therefore  require  the  more  skill  and  knowledge, 
and  those  in  the  greatest  variety,  from  skill  in  the  lowest  man- 


40 

ual  operation  to  knowledge  of  the  highest  exercise  of  the 
moral  functions  of  man,  that  they  may  perform  with  decency 
the  subordinate  duties  of  life,  and  be  qualified  to  govern 
the  state  in  the  true  spirit  of  its  constitution  and  laws. 
The  necessity  of  greater  knowledge  is  an  honorable  dis- 
tinction, but  the  acquisition  of  it  is  more  honorable ;  and 
the  adage  Ne  sutor  ultra  crepidam  is  wholly  inapplicable 
to  an  American  citizen.  Let  this  study,  therefore,  be  in- 
corporated with  the  other  useful  branches  in  the  general 
plan  of  the  popular  education,  in  order  to  complete  the  ba- 
sis of  a  system  commensurate  with  the  dignity  of  this 
form  of  government,  based  as  it  is  upon  the  inalienable 
rights  of  man. 

The  General  and  State  Governments  should  patronize  the 
general  diffusion  of  geometry  as  a  military  science. — The 
legislative  bodies  of  the  several  States,  as  well  as  the 
General  Government,  should  take  this  subject  into  their 
consideration.  In  the  cases  of  the  former,  there  are,  it  is 
believed,  no  constitutional  restrictions ;  we  are  not  aware 
that  their  authority  has  ever  been  questioned  as  regards  pro- 
viding by  law  for  the  education  of  their  citizens,  regulating 
the  matter  and  manner  of  that  education,  and  dispersing  the 
seeds  of  knowledge  freely  among  the  people. 

If,  however,  the  jealousy  of  the  States  should  deny  to 
Congress  such  a  construction  of  the  constitution  as  would 
empower  that  body  to  legislate  on  this  subject,  then  we 
would  inquire  upon  what  principle  they  act  when  they  re- 
serve so  many  sections  of  the  public  lands  for  the  purposes 
of  education  ?  wherefore  do  they  educate  one  youth  from 
each  congressional  district  at  a  military  school?  and  by 
what  authority  do  they  devote  their  time,  as  a  legislative 
body,  in  the  trusteeship  of  the  Smithsonian  bequest?  If 
Congress  may  appropriate  lands,  money,  and  time,  for  the 
diffusion  of  knowledge,  who  will  deny  them  the  power  of 
direction  as  to  the  characterof  that  knowledge?  Geometry 
is  the  basis  of  the  knowledge  of  the  most  feublime  sciences 


41 

known  to  the  human  mind,  and  the  best  adapted  to  the 
condition  of  a  free  people  ;  it  is  therefore  indispensable  in 
the  contemplation  of  any  institution  which  such  a  people 
might  be  expected  to  establish  for  the  diffusion  of  general 
knowledge.  Moreover,  it  is  that  science  which  is  most  con- 
genial with  a  condition  of  want  and  necessity,  and  most  ready- 
to  enter  as  one  of  the  principal  means  into  any  plan  for  the  im- 
provement of  humanity  in  its  rudest  state.  But  it  is  also  a 
military  science,  connected  with  the  defence  of  the  country  : 
if  it  be  expedient,  therefore,  to  diffuse  the  knowledge  of 
field  tactics,  it  is  expedient,  a  fortiori,  to  diffuse  that  of 
geometry,  which  includes  the  principles  generally  that  lie 
at  the  basis  of  the  art  of  war.  This  diffusion,  however,  can- 
not be  effected,  in  either  part,  through  the  single  officer  who 
graduates  at  West  Point :  therefore  the  militia,  to  whom  the 
country  belongs,  and  who  are  therefore  the  proper  defenders 
of  it,  must  remain  destitute  of  this  knowledge  so  necessary 
to  concert  of  action  in  the  day  of  trial  and  peril,  or  be  depend- 
ent upon  the  mercenary  skill  of  others  for  the  defence  of  their 
property  and  lives.  Again  :  if  it  be  the  province  of  Congress 
to  provide  by  law  for  organizing  companies,  battalions,  and 
regiments,  and  designating  their  commanders  ;  also  for  fur- 
nishing arms,  equipments,  and  rations, — is  it  not  likewise  the 
province  of  that  honorable  body  to  provide  for  the  diffusion 
of  such  knowledge  among  them  as  will  give  their  united 
action  the  desired  effect  ? 

To  the  National  Legislature,  therefore,  we  respectfully 
suggest  the  propriety  of  taking  into  their  consideration  the 
diffusion  of  this  elementary  knowledge  in  their  several  dis- 
tricts, through  the  medium  of  the  manual  and  chart  of 
geometry.  Let  the  junior  militia  participate  in  the  advan- 
tages of  this  military  science.  Out  of  many  thousands,  you 
educate  one :  this  is  well,  but  not  sufficient.  And  even  this 
scanty  provision  is  uncertain  ;  for  the  individual  whom  you 
select  may  be  less  worthy  of  command — may  be  rejected ; 
and  some  natural,  uninstruc ted  genius,  from  the  plough,  may 


n 

supersede  the  cadet  upon  whom  your  exclusive  patronage 
has  been  lavished.  Hi?ic  opera  et  irnpensa  peribunt.  Ed- 
ucate one,  and  neglect  ten  thousand,  and  be  disappointed  ! ! 
This  is  patriotism  inverted,  tapered  to  a  point,  attenuated  too 
finely  for  the  support  of  the  most  rarefied  aerial  existence. 
No7i  illud  opus  tenuissima  stamina  vincant. 

General  remarks  on  the  utilitarian  and  tranquilizing  char- 
acter of  the  study  of  geometry,  and  an  appeal  to  those  loho 
are  placed  in  a  good  position  to  aid  in  its  diffusion. — It 
is  desirable  that  the  plan  of  the  manual  and  chart  should 
be  submitted  to  trial  in  the  several  districts  of  the  United 
States ;  not  where  the  facilities  for  teaching  geometry  are 
already  furnished,  or  in  a  class  which  will  not  advance 
without  the  regular  demonstrations  ;  but  in  a  school,  or  class, 
which  will  proceed  to  collect  the  facts  connected  with  each 
proposition,  as  prescribed  in  a  preceding  part  of  this  Essay. 
This  trial  cannot,  however,  be  so  extensively  made,  with- 
out the  kind  and  efiicient  co-operation  of  the  members  of 
Congress.  We  are  therefore  anxious  to  enli&t  their  influence 
and  support  in  behalf  of  this  noble  cause.  The  magnitude 
of  the  enterprise  fills  us  with  regret  that  abler  talents  and 
more  propitious  circumstances  than  those  which  have  fallen 
to  our  lot  are  not  engaged  in  the  execution  of  it.  It  is  not 
the  high  refinements  of  science,  the  deep  research  of  philoso- 
phy, that  we  would  urge  on  the  public  attention;  it  is  the 
introduction  of  the  principles  of  geometry  into  the  schools — 
the  diflfusion  of  the  seeds  of  knowledge  where  they  are  not. 
Our  object  is  to  lay  the  foundation  of  the  national  educa- 
tion in  the  proper  and  sufficient  elements  ;  to  simplify  the 
incipient  means ;  to  scatter  the  good  seed  broadcast  in  town 
and  country,  and  send  thousands  of  youths  teeming  with 
the  germes  of  science  to  seek  the  fostering  instruction  of 
some  adjacent  Alma  Mater;  or,  should  that  be  out  of  their 
reach,  to  ascend  the  hill  of  science  by  their  own  application. 

Individual  influence,  however  great,  would  be  too  incon- 
siderable to  warrant  the  expectation  of  any  decided  action 


in  relation  to  this  important  work ;  its  merits  will  even  be 
rated  by  the  diminutive  proportions  of  those  of  our  agency, 
which  only  consist  in  a  zeal  for  the  promotion  of  the  cause  of 
science  that  has  increased  with  the  progressive  lapse  of  thirty- 
one  years.  It  is  now  our  belief,  based  on  the  experience  of 
many  vicissitudes,  that  the  perpetuation  of  the  principles  laid 
down  in  the  Declaration  of  Independence  depends  on  the 
more  equal  diffusion  of  knowledge,  the  disparity  of  which  has 
been  gradually  increasing  among  the  people  ;  that  mathe- 
matical science,  though  perhaps  defective  in  refinement, 
confers  a  greater  share  of  power  in  many  important  partic- 
ulars, and  is  therefore  the  best  among  the  available  means 
of  protection  against  any  encroachment  upon  social  rights  ; 
that  the  elements  of  this  knowledge  should  be  diffused, 
even  where  they  must  depend  solely  on  the  congeniality 
and  vigor  of  the  mental  soil  for  their  culture  and  improve- 
ment, trusting  that  skill  and  power  to  combine  and  employ 
them  would  soon  appear  in  the  native  genius  of  the  young 
people,  whom  we  cannot  thus  call  up  without  commending 
them  to  God.  We  are  further  of  opinion  that  the  studies 
which  we  here  desire  to  recommend,  if  carried  out  to  their 
legitimate  conclusions,  could  never  have  connexion  with 
metaphysics,  or  questions  of  uncertain  data,  and  consequent 
"  doubtful  disputation ;"  that  they  are  wholly  neutral  with 
respect  to  points  of  faith  which  may  be  controverted  by  the 
various  sects  in  polemical  divinity,  but  unequivocally  favor- 
able in  their  testimony  as  to  the  goodness,  wisdom,  and 
power  of  the  Creator  and  Governor  of  the  universe.  They 
are  therefore  incapable  of  being  employed  to  promote  dis- 
order in  communities,  of  which  the  inevitable  consequences 
are  usurpation  and  oppression  on  the  part  of  the  rulers,  un- 
less where  the  laws  are  sufficiently  powerful  to  restore  or- 
der to  the  body  politic.  Moreover,  in  the  lives  of  distin- 
guished mathematicians  which  have  been  handed  down  to 
us,  we  find  many  able  supporters  of  the  doctrines  of  Christ- 
ianity *,  and  there  is  just  reason  to  believe  that  many  more 


44 

have  erred,  in  doctrine  and  practice,  from  want  of  the 
knowledge  of  geometry,  than  from  its  superabundance. 

The  study  of  the  mathematics  comes  before  the  whole  peo- 
ple of  the  United  States,  not  a  thin  superstratum,  for  accept- 
ance or  rejection.  Where  neither  the  vis  inertice  of  the  matter, 
nor  the  fugitive  volatiHty  of  the  spirit  of  man,  resists  or 
evades  the  consideration  of  the  case,  the  want  of  power  in 
the  agency  will  be  sufficient  to  exclude  the  intended  ad- 
vantage. The  field  is  very  great,  and  the  laborers  must  be 
many.  Who,  then,  will  enlist  with  us  in  this  cause,  which 
has  for  its  object  the  greatest  amount  of  intellectual  and  moral 
good  ?  Will  the  members  of  the  legislature  refuse  to  con- 
vey intelligence  on  this  subject  to  the  friends  of  popular  edu- 
cation in  their  several  districts?  May  we  not  expect  the 
concurrence  of  the  distinguished  citizens  composing  the 
membership  of  the  National  Institution  in  this  laudable 
enterprise?  Here  is  a  definite  object  presented  for  their 
action,  and  one  which  lies  in  the  entrance  of  the  principal 
avenue  leading  to  the  Temple  of  the  Sciences.  The  means 
here  proposed  require  only  to  be  submitted  to  the  impartial 
test  of  practical  experiment ;  the  people  will  not  forego  the 
obvious  advantage  of  the  plan. 


TABLE  OF  CONTENTS. 


Page. 
Indications  of  the  desire  to  diffuse  knowledge— 

1.  In  the  action  of  Congress  with  regard  to  the  bequest  of  the  laie  Mr. 

Smithson 9 

9.  In  the  establishment  of  the  National  Institution  at  Washington 11 

3.  In  the  action  of  the  friends  of  popular  education  in  some  of  the  States, 

resulting  from  the  discoveries  made  in  the  last  census 12 

Astronomy,  which  leads  the  whole  train  of  the  sciences,  dependent  on 

the  elements  of  geometry < 13 

A  magazine  of  the  natural  sciences,  for  the  family  library,  should  com- 
mence with  the  elements  of  arithmetic  and  geometry. . .  # 15 

Geometry  and  arithmetic  should  have  priority  of  algebra 15 

The  magazine  should  explain  the  terms  which  involve  principles  in 

arithmetic  as  well  as  in  geometry 17 

An  explanation  of  the  true  principle  of  induction,  as  applicable  to  arith- 
metic      18 

The  leading  numbers  of  the  magazine  should  not  contain  abstruse  ques- 
tions      19 

Geometry  is  at  war  with  the  lawless  condition  of  mind  and  matter 20 

The  investigations  of  the  sciences  dependent  on  geometry  are  limited 
within  the  known  parts  of  the  creation ;  the  line  and  plummet  must 

never  be  out  of  use 21 

The  popular  education  is  defective  with  regard  to  means 22 

An  uneducated  population  are  the  materials  of  a  despotism., 22 

Domestic  education  is  the  most  available 23 

Equal  means  of  education  are  necessary  to  preserve  a  free  government, 

ami  avarice  is  its  antagonist 24 

Legislation  requires  intellectual  discipline  and  experience  of  the  rela- 
tions of  society. 25 

Concentration  and  diffusion  of  knowledge  contrtisted 26 

The  metaphorical  tree  of  knowledge 27 

School  commissioners  and  trustees  are  bound  to  lay  a  proper  foimdation 

for  public  instruction . . . , 28 

A  Chart  and  Manual  of  Geometry  for  the  use  of  schools  recommended    29 
A  description  of  the  Chart  and  Manual  of  Geometry,  with  the  title  of 

each,  and  the  supposed  terms  of  their  publication 30 

Geometry  and  arithmetic  .should  be  taught  at  the  same  time 31 


46 

Page 
The  efitire  labor  of  demonstration  should  not  be  at  once  imposed  on  the 

learner ;  it  should  be  classified 31 

Youth  is  the  proper  lime  for  acquiring  the  elements  of  science,  and 

forming  an  intelligent  ciiizen 32 

Geometry  taken  in  the  Euclidian  order  is  not  abstruse,  and  maybe 

learned  by  any  good  reader 32 

Teachers  may  acquire  this  knowledge  from  the  recitations  of  their 

pupils,  without  any  previous  study 33 

Colleges  have  a  pecuniary  interest  in  the  promotion  of  this  preparatoiy 

study 34 

Geometry  is  the  law  of  Nature,  as  it  regards  action  or  motion 34 

A  few  of  the  many  uses  of  geometry  to  a  free  people  enumerated 35 

The  study  of  geometry  produces  internal  order,  regulates  the  morals, 
and  elevates  the  mind  to  contemplate  the  sacred  order  of  the  Creator's 

works 36 

Good  government  is  a  Divine  unity;  and  a  freeman  must  either  exer- 
cise it  upon  himself,  or  fall  into  the  hands  of  another  master 37 

The  diagrams  and  propositions  of  geometry  should  be  every  where 

exhibited 38 

Geometry  is  necessary  to  complete  the  education  of  an  American  citizen    39 
The  General  and  State  Governments  should  patronize  the  general  dif- 
fusion of  geometry  as  a  military  science 40 

General  remarks  on  the  utilitarian  and  tranquilizing  character  of  the 
study  of  geometry,  and  an  appeal  to  those  who  are  placed  in  a  good 
position  to  aid  in  its  diffusion 42 

NoTB. — The  importance  of  this  subject,  included  in  the  general  tide,  may 
be  collected,  to  some  extent,  from  the  several  views  presented  in  the  pages 
of  this  pamphlet. 


1 


;6AYLORDBROS.  In*. 

SyT«cu»»,  N.  y. 

Stockton,  Caltf. 


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